1 Introduction

This script is structured as follows:

  • setup: loading packages and data
  • overview: displaying values such as N of participants, items, etc.
  • preprocessing: data wrangling steps
  • descriptive statistics: summary stats for said patterns
  • data visualization: visualizing the main data patterns we want to report
  • data visualization: covariates: plots for each covariate in relationship with IOS

Main bits necessary to understand the following analysis:

  • the column category differentiates abstract versus concrete
  • the column subcluster differentiates different types of abstract and concrete concepts
  • the two main dependent variables are closeness and IOS (self-other inclusion)

The following baseline analyses will be performed:

  • assess correlations between covariates
  • assess the effect of all covariates on IOS
  • assess the effect of all covariates on closeness

The following main analyses will be performed:

  • assess the interaction of category and other_inclusion on IOS
  • assess the interaction of category and other_inclusion on closeness
  • assess the interaction of category and self_inclusion on IOS
  • assess the interaction of category and self_inclusion on closeness
  • repeat all those models for subcluster to zoom into the more detailed category structure of abstract concepts

We will look additionally also at difficulty:

  • assess the effect of category on difficulty, and in a separate model of subcluster
  • perform both main analyses again, this time controlling for difficulty

For all brms model fits, corresponding code chunks are set to eval = FALSE in the final file with pre-compiled models saved in models folder that are loaded into this script to save the user time.

2 Setup

Load packages:

library(tidyverse) # for data processing
library(brms) # for Bayesian mixed models
library(tidybayes) # for half-eye plots of posteriors
library(ggridges) # for joy plots
library(patchwork) # for multiplot arrays
library(gridExtra) # for multiplot arrays when patchwork fails us
library(plotly) # for scatterplot matrix
library(GGally) # for scatterplot matrix

Load data:

# Load data:

df <- read_csv('../data/abstract_concepts_conversations_all_E2.csv')

# Show some random rows:

sample_n(df, 5)
## # A tibble: 5 × 13
##   participant word       category subcluster passive_closeness active_closeness
##         <dbl> <chr>      <chr>    <chr>                  <dbl>            <dbl>
## 1         136 Cactus     Concrete Conc_an                 83               81.1
## 2         115 Cactus     Concrete Conc_an                 79.6             77.6
## 3          26 Zucca      Concrete Conc_an                 88.9             90.2
## 4          94 Abitudine  Abstract SS                      43.4             48.1
## 5          57 Giuramento Abstract EM                      96.4             96  
## # ℹ 7 more variables: pleasantness <dbl>, commitment <dbl>, intimacy <dbl>,
## #   difficulty <dbl>, self_contribution <dbl>, other_contribution <dbl>,
## #   IOS <dbl>

3 Data cleaning and processing

For the main model later, we want to look at how category influences IOS when interacting with other_contribution. For this we need to center other_contribution first. We’ll do this here already so that subsets of this data also contain the centered covariate other_contribution_c. We’ll later also use difficulty as a control covariate, so let’s center that as well just in case.

df <- mutate(df,
             other_contribution_c = other_contribution - mean(other_contribution,
                                                              na.rm = TRUE),
             self_contribution_c = self_contribution - mean(self_contribution,
                                                            na.rm = TRUE),
             difficulty_c = difficulty - mean(difficulty,
                                              na.rm = TRUE))

Also change the content of the category column so that the labels say abstract and concrete, and make the latter come first, which is more intuitive:

df <- mutate(df,
             category = str_to_lower(category),
             category = factor(category,
                               levels = c('concrete', 'abstract')))

Check the content of the subcluster column, which contains more detailed breakdowns of different kinds of concepts.

df %>% 
  count(subcluster)
## # A tibble: 6 × 2
##   subcluster     n
##   <chr>      <int>
## 1 Conc_an      278
## 2 Conc_in      266
## 3 EM           174
## 4 PS           136
## 5 PSTQ         136
## 6 SS            98
# Compare:

df %>% 
  count(category)
## # A tibble: 2 × 2
##   category     n
##   <fct>    <int>
## 1 concrete   544
## 2 abstract   544

Slightly uneven distribution for the different subclusters, with relatively fewer SS concepts (= self-sociality), and slightly more EM concepts (= emotional).

Let’s give them more transparent labels, which is also useful for plotting later. We’ll call the new column spellout, because it “spells out” the abbreviations.

df <- mutate(df,
             spellout = case_when(
               subcluster == 'Conc_an'~ 'concrete animate or organic',
               subcluster == 'Conc_in'~ 'concrete inanimate or inorganic',
               subcluster == 'EM'~ 'abstract emotional',
               subcluster == 'PSTQ'~ 'abstract quantitative-temporal-spatial',
               subcluster == 'PS'~ 'abstract philosophical-spiritual',
               subcluster == 'SS'~ 'abstract self-sociality'
             ))

Check the correlation between active and passive closeness:

with(df, cor.test(active_closeness, passive_closeness))
## 
##  Pearson's product-moment correlation
## 
## data:  active_closeness and passive_closeness
## t = 89.297, df = 1086, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9306087 0.9449012
## sample estimates:
##       cor 
## 0.9381534

r = 0.94, very highly correlated. Let’s average them for the main analysis. The new variable will be called closeness, and the average of active_closeness and passive_closeness.

df <- mutate(df,
             closeness = (active_closeness + passive_closeness) / 2)

The closeness dependent measure is a VAS scale between 0 and 100. This needs to be scaled to [0, 1] for the beta distribution. We will call the new variable that is scaled this way closeness_01.

df <- mutate(df, closeness_01 = closeness / 100)

4 Overview, preprocessing, and exclusions

Check participants prior to exclusion:

# Count rows per participants:

df %>% 
  count(participant)
## # A tibble: 136 × 2
##    participant     n
##          <dbl> <int>
##  1           1     8
##  2           2     8
##  3           3     8
##  4           4     8
##  5           5     8
##  6           6     8
##  7           7     8
##  8           8     8
##  9           9     8
## 10          10     8
## # ℹ 126 more rows
# Count rows of this table to print number of participants into console:

df %>% 
  count(participant) %>% 
  nrow()
## [1] 136

136 participants.

Let’s exclude the participants that are meant to be excluded. This information comes directly from Chiara, and specifically, I am supposed to exclude participants 72, 8, 74, 129, 111, 55, and 53. We’ve checked these and they do indeed look odd, seemingly responding like straightliners.

# Define exclusion vector:

bad_ones <- c(72, 8, 74, 129, 111, 55, 53)

# Exclude:

df <- filter(df,
             !(participant %in% bad_ones))

# Check:

df %>% 
  count(participant) %>% 
  nrow()
## [1] 129

Seven participants less, which is correct.

Now let’s do the same for words (= items):

# Count rows per participants:

df %>% 
  count(word)
## # A tibble: 32 × 2
##    word           n
##    <chr>      <int>
##  1 Abitudine     31
##  2 Aereo         31
##  3 Attenzione    30
##  4 Bottiglia     31
##  5 Brivido       35
##  6 Cactus        30
##  7 Causa         31
##  8 Enigma        33
##  9 Fama          35
## 10 Favola        35
## # ℹ 22 more rows
# Count rows of this table to print number of participants into console:

df %>% 
  count(word) %>% 
  nrow()
## [1] 32

32 items.

What are these words?

distinct(df, subcluster, word) %>% 
  sample_n(20)
## # A tibble: 20 × 2
##    subcluster word      
##    <chr>      <chr>     
##  1 PS         Tendenza  
##  2 Conc_an    Cactus    
##  3 Conc_in    Tavolo    
##  4 EM         Favola    
##  5 Conc_an    Gallo     
##  6 EM         Giuramento
##  7 Conc_in    Aereo     
##  8 PS         Causa     
##  9 Conc_in    Quaderno  
## 10 PSTQ       Brivido   
## 11 Conc_an    Pescatore 
## 12 Conc_an    Turista   
## 13 PS         Enigma    
## 14 Conc_an    Insalata  
## 15 EM         Scherzo   
## 16 Conc_in    Pentola   
## 17 Conc_an    Zucca     
## 18 PSTQ       Inizio    
## 19 Conc_an    Sarto     
## 20 SS         Attenzione

For presentation purposes only, dichotomize the other_contribution variable, and order it in such a way that low other comes before high other. This will be used in the median_split_p code chunk below as well.

# Calculate median:

md <- median(df$other_contribution)

# Create median split variable:

df <- mutate(df,
             other_cat = ifelse(other_contribution > md,
                                'high other contribution',
                                'low other contribution'),
             other_cat = factor(other_cat,
                                levels = c('low other contribution',
                                           'high other contribution')))

Let’s look at the average IOS for abstract and concrete as a function of the median split:

df %>% 
  group_by(other_cat, category) %>% 
  summarize(M_IOS = mean(IOS),
            M_dist = mean(closeness))
## `summarise()` has grouped output by 'other_cat'. You can override using the
## `.groups` argument.
## # A tibble: 4 × 4
## # Groups:   other_cat [2]
##   other_cat               category M_IOS M_dist
##   <fct>                   <fct>    <dbl>  <dbl>
## 1 low other contribution  concrete  3.03   65.8
## 2 low other contribution  abstract  2.91   66.0
## 3 high other contribution concrete  3.52   73.5
## 4 high other contribution abstract  3.66   74.5

Although it only comes up later, we’ll set the reference levels for subcluster here now:

df <- mutate(df,
             subcluster = factor(subcluster),
             subcluster = relevel(subcluster, ref = 'PSTQ'))

# Check:

levels(df$subcluster)
## [1] "PSTQ"    "Conc_an" "Conc_in" "EM"      "PS"      "SS"

5 Descriptive statistics

Calculate closeness as a function of category and subcluster:

# Category (abstract versus concrete):

df %>% 
  group_by(category) %>% 
  summarize(M = mean(closeness))
## # A tibble: 2 × 2
##   category     M
##   <fct>    <dbl>
## 1 concrete  69.8
## 2 abstract  70.1
# Subcluster:

df %>% 
  group_by(spellout) %>% 
  summarize(M = mean(closeness)) %>% 
  arrange(desc(M))
## # A tibble: 6 × 2
##   spellout                                   M
##   <chr>                                  <dbl>
## 1 abstract quantitative-temporal-spatial  70.7
## 2 abstract emotional                      70.5
## 3 concrete animate or organic             70.3
## 4 abstract philosophical-spiritual        69.5
## 5 abstract self-sociality                 69.4
## 6 concrete inanimate or inorganic         69.2

Check self_contribution and other_contribution for the different subclusters. Chiara says that self-sociality and emotional abstract concepts should be more interacting with self-contribution, and philosophical more with other-contribution.

# Self contribution:

df %>% 
  group_by(spellout) %>% 
  summarize(self = mean(self_contribution)) %>% 
  arrange(desc(self))
## # A tibble: 6 × 2
##   spellout                                self
##   <chr>                                  <dbl>
## 1 concrete inanimate or inorganic         71.3
## 2 abstract self-sociality                 71.0
## 3 abstract philosophical-spiritual        70.7
## 4 abstract quantitative-temporal-spatial  70.4
## 5 abstract emotional                      70.1
## 6 concrete animate or organic             69.4
# Other contribution:

df %>% 
  group_by(spellout) %>% 
  summarize(other = mean(other_contribution)) %>% 
  arrange(desc(other))
## # A tibble: 6 × 2
##   spellout                               other
##   <chr>                                  <dbl>
## 1 abstract quantitative-temporal-spatial  69.5
## 2 abstract emotional                      69.4
## 3 concrete animate or organic             69.1
## 4 concrete inanimate or inorganic         68.9
## 5 abstract self-sociality                 68.4
## 6 abstract philosophical-spiritual        67.2

“Philosophical-spiritual” is actually least high on other contribution. “Self-sociality” is high on self contribution, but emotional not so much. Overall, the average differences between these categories are relatively small.

Calculate IOS as a function of category and spellout:

# Abstract versus concrete:

df %>% 
  group_by(category) %>% 
  summarize(M = mean(IOS))
## # A tibble: 2 × 2
##   category     M
##   <fct>    <dbl>
## 1 concrete  3.28
## 2 abstract  3.27
# Different sub groups:

df %>% 
  group_by(subcluster) %>% 
  summarize(M = mean(IOS)) %>% 
  arrange(desc(M))
## # A tibble: 6 × 2
##   subcluster     M
##   <fct>      <dbl>
## 1 EM          3.38
## 2 Conc_in     3.29
## 3 PSTQ        3.29
## 4 Conc_an     3.28
## 5 PS          3.19
## 6 SS          3.18

Raw descriptive correlation between covariates:

# Extract covariates into one object:

covs <- df %>% 
  select(pleasantness:other_contribution)

# Perform pairwise correlations for all covariates:

round(cor(covs), 2)
##                    pleasantness commitment intimacy difficulty
## pleasantness               1.00       0.54     0.53      -0.37
## commitment                 0.54       1.00     0.53      -0.18
## intimacy                   0.53       0.53     1.00      -0.23
## difficulty                -0.37      -0.18    -0.23       1.00
## self_contribution          0.45       0.64     0.44      -0.21
## other_contribution         0.59       0.54     0.43      -0.19
##                    self_contribution other_contribution
## pleasantness                    0.45               0.59
## commitment                      0.64               0.54
## intimacy                        0.44               0.43
## difficulty                     -0.21              -0.19
## self_contribution               1.00               0.64
## other_contribution              0.64               1.00

The highest correlations are between self_contribution and commitment, followed by other_contribution and pleasantness.

For the description of IOS as a function of the different covariates, I think it would be most intuitive to talk about the means of the highest and lowest scale points, as well as perhaps report Spearman’s rho. Let’s do that for each covariate in turn.

Pleasantness:

df %>% 
  group_by(IOS) %>% 
  summarize(M = mean(pleasantness))
## # A tibble: 6 × 2
##     IOS     M
##   <dbl> <dbl>
## 1     1  36.8
## 2     2  55.6
## 3     3  66.9
## 4     4  72.6
## 5     5  82.4
## 6     6  89.7
with(df, cor(IOS, pleasantness, method = 'spearman'))
## [1] 0.5265202

Commitment:

df %>% 
  group_by(IOS) %>% 
  summarize(M = mean(commitment))
## # A tibble: 6 × 2
##     IOS     M
##   <dbl> <dbl>
## 1     1  64.4
## 2     2  69.1
## 3     3  72.6
## 4     4  74.0
## 5     5  80.1
## 6     6  83.6
with(df, cor(IOS, commitment, method = 'spearman'))
## [1] 0.2232285

Intimacy:

df %>% 
  group_by(IOS) %>% 
  summarize(M = mean(intimacy))
## # A tibble: 6 × 2
##     IOS     M
##   <dbl> <dbl>
## 1     1  52.6
## 2     2  57.2
## 3     3  64.2
## 4     4  59.7
## 5     5  72.1
## 6     6  79.9
with(df, cor(IOS, intimacy, method = 'spearman'))
## [1] 0.2034185

Difficulty:

df %>% 
  group_by(IOS) %>% 
  summarize(M = mean(difficulty, na.rm = TRUE))
## # A tibble: 6 × 2
##     IOS     M
##   <dbl> <dbl>
## 1     1  44.3
## 2     2  34.7
## 3     3  32.0
## 4     4  30.1
## 5     5  22.3
## 6     6  15.8
with(df, cor(IOS, difficulty,
             method = 'spearman',
             use = 'complete.obs'))
## [1] -0.2375146

Self-contribution:

df %>% 
  group_by(IOS) %>% 
  summarize(M = mean(self_contribution, na.rm = TRUE))
## # A tibble: 6 × 2
##     IOS     M
##   <dbl> <dbl>
## 1     1  67.7
## 2     2  67.2
## 3     3  68.7
## 4     4  70.8
## 5     5  76.0
## 6     6  81.5
with(df, cor(IOS, self_contribution,
             method = 'spearman',
             use = 'complete.obs'))
## [1] 0.1914012

Other-contribution:

df %>% 
  group_by(IOS) %>% 
  summarize(M = mean(other_contribution, na.rm = TRUE))
## # A tibble: 6 × 2
##     IOS     M
##   <dbl> <dbl>
## 1     1  60.2
## 2     2  63.6
## 3     3  68.0
## 4     4  71.1
## 5     5  75.2
## 6     6  82.2
with(df, cor(IOS, other_contribution,
             method = 'spearman',
             use = 'complete.obs'))
## [1] 0.2567562

6 Data visualization

Make a plot of IOS as a function of category (= concept type, abstract v concrete).

# Plot core:

category_ios_p <- df %>% 
  count(IOS, category) %>% 
  ggplot(aes(x = IOS, y = n, fill = category)) +
  geom_col(position = 'dodge', width = 0.7,
           col = 'black', size = 0.3)
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
# Scales and axes:

category_ios_p <- category_ios_p +
  scale_fill_manual(values = c('grey55', 'purple2')) +
  scale_x_continuous(expand = c(0, 0),
                     limits = c(0, 7),
                     breaks = 1:6) +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 160),
                     breaks = seq(0, 160, 20)) +
  ylab('Number of responses') +
  xlab('IOS (self-other inclusion test)')

# Cosmetic tweaking:

category_ios_p <- category_ios_p +
  theme_classic() +
  theme(legend.position = 'top',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show in markdown and save in folder:

category_ios_p

ggsave(plot = category_ios_p,
       filename = '../figures_E2/category_ios_E2.pdf',
       width = 5, height = 3.5)

Make a plot of this with a facet wrap for the median split:

# Plot core:

median_split_p <- df %>% 
  count(IOS, other_cat, category) %>% 
  ggplot(aes(x = IOS, y = n, fill = category)) +
  geom_bar(position = 'fill', width = 0.7,
           stat = 'identity',
           col = 'black', size = 0.3) +
  facet_wrap(~other_cat, ncol = 2)

# Scales and axes:

median_split_p <- median_split_p +
  scale_fill_manual(values = c('goldenrod3', 'steelblue')) +
  scale_y_continuous(expand = c(0, 0)) +
  ylab('Proportion') +
  xlab('IOS (self-other inclusion test)')

# Cosmetic tweaking:

median_split_p <- median_split_p +
  theme_classic() +
  theme(legend.position = 'top',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)),
        plot.margin = margin(r = 100))

# Show in markdown and save in folder:

median_split_p

ggsave(plot = median_split_p,
       filename = '../figures_E2/median_split_E2_p.pdf',
       width = 7, height = 3)

Copy and paste the code from Experiment 1 here to reproduce the bin plot:

df <- mutate(df,
             other_bin2 = cut_number(other_contribution, 4))

# Redo the averages:

bin_avgs <- df %>% 
  group_by(other_bin2, category) %>% 
  summarize(IOS_M = mean(IOS),
            IOS_SD = sd(IOS))
## `summarise()` has grouped output by 'other_bin2'. You can override using the
## `.groups` argument.
# Append counts so that we can compute simple standard errors of the mean:

bin_counts <- df %>% 
  count(other_bin2, category)

# Join together:

bin_avgs <- left_join(bin_avgs, bin_counts)
## Joining with `by = join_by(other_bin2, category)`
# Compute standard errors:

bin_avgs <- mutate(bin_avgs, 
                   SE = IOS_SD / sqrt(n),
                   lower = IOS_M - SE,
                   upper = IOS_M + SE,
                   lower_CI = IOS_M - 1.96 * SE,
                   upper_CI = IOS_M + 1.96 * SE)

Let’s do that new bin plot:

# Plot core:

bin_p <- bin_avgs %>% 
  ggplot(aes(x = other_bin2, y = IOS_M,
             color = category, group = category)) +
  geom_line(size = 0.8) +
  geom_point(pch = 15, size = 2,
             position = position_dodge(width = 0.1)) +
  geom_errorbar(aes(ymin = lower_CI, ymax = upper_CI),
                width = 0,
                position = position_dodge(width = 0.1))

# Scales and axes:

bin_p <- bin_p +
  scale_color_manual(values = c('goldenrod3', 'steelblue')) +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(2, 4.5),
                     breaks = seq(2, 4.5, 0.5)) +
  ylab('IOS mean') +
  xlab('Other contribution (binned)') +
  annotate(geom = 'text',
           label = 'concrete concepts',
           color = 'goldenrod3',
           x = 0.7, y = 3.25,
           hjust = 0, size = 3) +
  annotate(geom = 'text',
           label = 'abstract concepts',
           color = 'steelblue',
           x = 0.7, y = 2.51,
           hjust = 0, size = 3)

# Cosmetic tweaking:

bin_p <- bin_p +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show in markdown and save in folder:

bin_p

ggsave(plot = bin_p,
       filename = '../figures_E2/IOS_equal_bin_plot.pdf',
       width = 4.5, height = 3.4)

7 Data visualization: covariates, and covariates with IOS

Scatter plot matrix for covariates:

# Setings for diagonal:

diag_wrap <- wrap("densityDiag", alpha = 0.5,
                  fill = 'steelblue')

# Plot core:

scatter_p <- ggpairs(covs,
                     aes(alpha = 0.5),
                     diag = list(continuous = diag_wrap))

# Cosmetics:

scatter_p <- scatter_p +
  theme_minimal()

# Show in markdown and save in folder:

scatter_p

ggsave(plot = scatter_p,
       filename = '../figures_E2/covariate_matrix_E2.pdf',
       width = 8, height = 8)

Pleasantness and IOS:

# Plot core:

pleasant_joy_p <- df %>% 
  ggplot(aes(x = pleasantness, y = factor(IOS))) +
  geom_density_ridges(fill = 'steelblue',
                      jittered_points = TRUE,
                      position = position_points_jitter(width = 0.05,
                                                        height = 0),
                      point_shape = '|', point_size = 2,
                      point_alpha = 1, alpha = 0.7)

# Scales and axes:

pleasant_joy_p <- pleasant_joy_p +
  ylab('IOS\n(inclusion of other scale)') +
  xlab('Pleasantness') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-20, +120))

# Cosmetic tweaking:

pleasant_joy_p <- pleasant_joy_p +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show in markdown and save in folder:

pleasant_joy_p
## Picking joint bandwidth of 5.67

ggsave(plot = pleasant_joy_p,
       filename = '../figures_E2/pleasantness_joy_E2.pdf',
       width = 5, height = 3.5)
## Picking joint bandwidth of 5.67

Commitment and IOS:

# Plot core:

commit_joy_p <- df %>% 
  ggplot(aes(x = commitment, y = factor(IOS))) +
  geom_density_ridges(fill = 'steelblue',
                      jittered_points = TRUE,
                      position = position_points_jitter(width = 0.05,
                                                        height = 0),
                      point_shape = '|', point_size = 2,
                      point_alpha = 1, alpha = 0.7)

# Scales and axes:

commit_joy_p <- commit_joy_p +
  ylab('IOS\n(inclusion of other scale)') +
  xlab('Commitment') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-20, +120))

# Cosmetic tweaking:

commit_joy_p <- commit_joy_p +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show in markdown and save in folder:

commit_joy_p
## Picking joint bandwidth of 6.22
## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).

ggsave(plot = commit_joy_p,
       filename = '../figures_E2/commitment_joy_E2.pdf',
       width = 4.5, height = 4)
## Picking joint bandwidth of 6.22
## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).

Intimacy and IOS:

# Plot core:

intimate_joy_p <- df %>% 
  ggplot(aes(x = intimacy, y = factor(IOS))) +
  geom_density_ridges(fill = 'steelblue',
                      jittered_points = TRUE,
                      position = position_points_jitter(width = 0.05,
                                                        height = 0),
                      point_shape = '|', point_size = 2,
                      point_alpha = 1, alpha = 0.7)

# Scales and axes:

intimate_joy_p <- intimate_joy_p +
  ylab('IOS\n(inclusion of other scale)') +
  xlab('Intimacy') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-20, +120))

# Cosmetic tweaking:

intimate_joy_p <- intimate_joy_p +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show in markdown and save in folder:

intimate_joy_p
## Picking joint bandwidth of 8.47

ggsave(plot = intimate_joy_p,
       filename = '../figures_E2/intimacy_joy_E2.pdf',
       width = 4.5, height = 4)
## Picking joint bandwidth of 8.47

Difficulty and IOS:

# Plot core:

difficult_joy_p <- df %>% 
  ggplot(aes(x = difficulty, y = factor(IOS)))+
  geom_density_ridges(fill = 'steelblue',
                      jittered_points = TRUE,
                      position = position_points_jitter(width = 0.05,
                                                        height = 0),
                      point_shape = '|', point_size = 2,
                      point_alpha = 1, alpha = 0.7)

# Scales and axes:

difficult_joy_p <- difficult_joy_p +
  ylab('IOS\n(inclusion of other scale)') +
  xlab('Difficulty') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-20, +120))

# Cosmetic tweaking:

difficult_joy_p <- difficult_joy_p +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show in markdown and save in folder:

difficult_joy_p
## Picking joint bandwidth of 7.04

ggsave(plot = difficult_joy_p,
       filename = '../figures_E2/difficulty_joy_E2.pdf',
       width = 4.5, height = 4)
## Picking joint bandwidth of 7.04

Self contribution and IOS:

# Plot core:

self_joy_p <- df %>% 
  ggplot(aes(x = self_contribution, y = factor(IOS))) +
  geom_density_ridges(fill = 'steelblue',
                      jittered_points = TRUE,
                      position = position_points_jitter(width = 0.05,
                                                        height = 0),
                      point_shape = '|', point_size = 2,
                      point_alpha = 1, alpha = 0.7)

# Scales and axes:

self_joy_p <- self_joy_p +
  ylab('IOS\n(inclusion of other scale)') +
  xlab('Self contribution') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-20, +120))

# Cosmetic tweaking:

self_joy_p <- self_joy_p +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show in markdown and save in folder:

self_joy_p
## Picking joint bandwidth of 6.46
## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).

ggsave(plot = self_joy_p,
       filename = '../figures_E2/self_joy_E2.pdf',
       width = 4.5, height = 4)
## Picking joint bandwidth of 6.46
## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).

Other contribution and IOS:

# Plot core:

other_joy_p <- df %>% 
  ggplot(aes(x = other_contribution, y = factor(IOS))) +
  geom_density_ridges(fill = 'steelblue',
                      jittered_points = TRUE,
                      position = position_points_jitter(width = 0.05,
                                                        height = 0),
                      point_shape = '|', point_size = 2,
                      point_alpha = 1, alpha = 0.7)

# Scales and axes:

other_joy_p <- other_joy_p +
  ylab('IOS\n(inclusion of other scale)') +
  xlab('Other contribution') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-20, +120))

# Cosmetic tweaking:

other_joy_p <- other_joy_p +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show in markdown and save in folder:

other_joy_p
## Picking joint bandwidth of 6.53

ggsave(plot = other_joy_p,
       filename = '../figures_E2/other_joy_E2.pdf',
       width = 4.5, height = 4)
## Picking joint bandwidth of 6.53

Make a plot matrix out of all of these:

# Define layout matrix:

my_layout <- matrix(c(1, 2, 3,
                      4, 5, 6),
                    byrow = TRUE, ncol = 3)

# Change titles:

commit_joy_p <- commit_joy_p +
  ylab(NULL)
intimate_joy_p <- intimate_joy_p +
  ylab(NULL)
self_joy_p <- self_joy_p +
  ylab(NULL)
other_joy_p <- other_joy_p +
  ylab(NULL)

# Show:

grid.arrange(pleasant_joy_p, commit_joy_p, intimate_joy_p,
             difficult_joy_p, self_joy_p, other_joy_p,
             layout_matrix = my_layout)

# Save:

all_joy <- arrangeGrob(pleasant_joy_p, commit_joy_p, intimate_joy_p,
                       difficult_joy_p, self_joy_p, other_joy_p,
                       layout_matrix = my_layout)

# Save:

all_joy <- arrangeGrob(pleasant_joy_p, commit_joy_p, intimate_joy_p,
                       difficult_joy_p, self_joy_p, other_joy_p,
                       layout_matrix = my_layout)

ggsave(all_joy, file = '../figures_E2/all_covariate_joy_E2.pdf',
       width = 12, height = 6)

8 Data visualization: scatterplots of covariates with closeness

Scatterplot matrix of all variables. First, let’s start with pleasantness:

pleasant_scatter <- df |> 
  ggplot(aes(x = pleasantness, y = closeness)) +
  geom_smooth(method = 'lm', col = 'purple',
              se = FALSE, size = 1.5) +
  geom_point()

# Scales and axes:

pleasant_scatter <- pleasant_scatter +
  ylab('Closeness') +
  xlab('Pleasantness') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-5, +105))

# Cosmetic tweaking:

pleasant_scatter <- pleasant_scatter +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show and save:

pleasant_scatter
## `geom_smooth()` using formula = 'y ~ x'

ggsave(filename = '../figures_E2/E2_pleasant_scatter.pdf', plot = pleasant_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'
ggsave(filename = '../figures_E2/E2_pleasant_scatter.png', plot = pleasant_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'

Second, commitment:

commitment_scatter <- df |> 
  ggplot(aes(x = commitment, y = closeness)) +
  geom_smooth(method = 'lm', col = 'purple',
              se = FALSE, size = 1.5) +
  geom_point()

# Scales and axes:

commitment_scatter <- commitment_scatter +
  ylab('Closeness') +
  xlab('Pleasantness') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-5, +105))

# Cosmetic tweaking:

commitment_scatter <- commitment_scatter +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show and save:

commitment_scatter
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Warning: Removed 1 rows containing missing values (`geom_point()`).

ggsave(filename = '../figures_E2/E2_commitment_scatter.pdf',
       plot = commitment_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Removed 1 rows containing missing values (`geom_point()`).
ggsave(filename = '../figures_E2/E2_commitment_scatter.png',
       plot = commitment_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Removed 1 rows containing missing values (`geom_point()`).

Third, intimacy:

intimacy_scatter <- df |> 
  ggplot(aes(x = intimacy, y = closeness)) +
  geom_smooth(method = 'lm', col = 'purple',
              se = FALSE, size = 1.5) +
  geom_point()

# Scales and axes:

intimacy_scatter <- intimacy_scatter +
  ylab('Closeness') +
  xlab('Pleasantness') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-5, +105))

# Cosmetic tweaking:

intimacy_scatter <- intimacy_scatter +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show and save:

intimacy_scatter
## `geom_smooth()` using formula = 'y ~ x'

ggsave(filename = '../figures_E2/E2_intimacy_scatter.pdf',
       plot = intimacy_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'
ggsave(filename = '../figures_E2/E2_intimacy_scatter.png',
       plot = intimacy_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'

Fourth, difficulty:

difficulty_scatter <- df |> 
  ggplot(aes(x = difficulty, y = closeness)) +
  geom_smooth(method = 'lm', col = 'purple',
              se = FALSE, size = 1.5) +
  geom_point()

# Scales and axes:

difficulty_scatter <- difficulty_scatter +
  ylab('Closeness') +
  xlab('Pleasantness') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-5, +105))

# Cosmetic tweaking:

difficulty_scatter <- difficulty_scatter +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show and save:

difficulty_scatter
## `geom_smooth()` using formula = 'y ~ x'

ggsave(filename = '../figures_E2/E2_difficulty_scatter.pdf',
       plot = difficulty_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'
ggsave(filename = '../figures_E2/E2_difficulty_scatter.png',
       plot = difficulty_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'

Fifth, self-contribution:

self_contribution_scatter <- df |> 
  ggplot(aes(x = self_contribution, y = closeness)) +
  geom_smooth(method = 'lm', col = 'purple',
              se = FALSE, size = 1.5) +
  geom_point()

# Scales and axes:

self_contribution_scatter <- self_contribution_scatter +
  ylab('Closeness') +
  xlab('Pleasantness') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-5, +105))

# Cosmetic tweaking:

self_contribution_scatter <- self_contribution_scatter +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show and save:

self_contribution_scatter
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Warning: Removed 1 rows containing missing values (`geom_point()`).

ggsave(filename = '../figures_E2/E2_self_contribution_scatter.pdf',
       plot = self_contribution_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Removed 1 rows containing missing values (`geom_point()`).
ggsave(filename = '../figures_E2/E2_self_contribution_scatter.png',
       plot = self_contribution_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Removed 1 rows containing missing values (`geom_point()`).

Sixth, other-contribution:

other_contribution_scatter <- df |> 
  ggplot(aes(x = other_contribution, y = closeness)) +
  geom_smooth(method = 'lm', col = 'purple',
              se = FALSE, size = 1.5) +
  geom_point()

# Scales and axes:

other_contribution_scatter <- other_contribution_scatter +
  ylab('Closeness') +
  xlab('Pleasantness') +
  scale_x_continuous(breaks = seq(0, 100, 20),
                     limits = c(-5, +105))

# Cosmetic tweaking:

other_contribution_scatter <- other_contribution_scatter +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show and save:

other_contribution_scatter
## `geom_smooth()` using formula = 'y ~ x'

ggsave(filename = '../figures_E2/E2_other_contribution_scatter.pdf',
       plot = other_contribution_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'
ggsave(filename = '../figures_E2/E2_other_contribution_scatter.png',
       plot = other_contribution_scatter,
       width = 4.5, height = 4)
## `geom_smooth()` using formula = 'y ~ x'

Put everything together into a big plot matrix:

# Define layout matrix:

my_layout <- matrix(c(1, 2, 3,
                      4, 5, 6),
                    byrow = TRUE, ncol = 3)

# Change titles:

commitment_scatter <- commitment_scatter +
  ylab(NULL)
intimacy_scatter <- intimacy_scatter +
  ylab(NULL)
self_contribution_scatter <- self_contribution_scatter +
  ylab(NULL)
other_contribution_scatter <- other_contribution_scatter +
  ylab(NULL)

# Show:

grid.arrange(pleasant_scatter, commitment_scatter, intimacy_scatter,
             difficulty_scatter, self_contribution_scatter, other_contribution_scatter,
             layout_matrix = my_layout)

# Save:

all_joy <- arrangeGrob(pleasant_scatter, commitment_scatter, intimacy_scatter,
                       difficulty_scatter, self_contribution_scatter, other_contribution_scatter,
                       layout_matrix = my_layout)

ggsave(all_joy, file = '../figures_E2/all_covariate_closeness.pdf',
       width = 12, height = 6)
ggsave(all_joy, file = '../figures_E2/all_covariate_closeness.png',
       width = 12, height = 6)

9 Covariate models

Make a model of all covariates on IOS:

covariates_IOS_mdl <- brm(IOS ~ 
                            
                            # Fixed effects:
                            
                            1 +
                            pleasantness +
                            commitment +
                            intimacy +
                            difficulty + 
                            self_contribution +
                            other_contribution +
                            
                            # Random effects:
                            
                            (1|participant) +
                            (0 + pleasantness|participant) +
                            (0 + commitment|participant) +
                            (0 + intimacy|participant) +
                            (0 + difficulty|participant) +
                            (0 + self_contribution|participant) +
                            (0 + other_contribution|participant) +
                            (1|word),
                          
                          # General stuff:
           
                          data = df,
                          family = cumulative,
           
                          # MCMC settings:
           
                          seed = 42,
                          cores = 4,
                          iter = 6000,
                          warmup = 3000,
                          control = list(adapt_delta = 0.9))

# Save model:

save(covariates_IOS_mdl, file = '../models_E2/covariates_IOS_mdl.Rdata')

Load:

load('../models_E2/covariates_IOS_mdl.Rdata')

Show priors:

prior_summary(covariates_IOS_mdl)
##                 prior     class               coef       group resp dpar nlpar
##                (flat)         b                                               
##                (flat)         b         commitment                            
##                (flat)         b         difficulty                            
##                (flat)         b           intimacy                            
##                (flat)         b other_contribution                            
##                (flat)         b       pleasantness                            
##                (flat)         b  self_contribution                            
##  student_t(3, 0, 2.5) Intercept                                               
##  student_t(3, 0, 2.5) Intercept                  1                            
##  student_t(3, 0, 2.5) Intercept                  2                            
##  student_t(3, 0, 2.5) Intercept                  3                            
##  student_t(3, 0, 2.5) Intercept                  4                            
##  student_t(3, 0, 2.5) Intercept                  5                            
##  student_t(3, 0, 2.5)        sd                                               
##  student_t(3, 0, 2.5)        sd                    participant                
##  student_t(3, 0, 2.5)        sd         commitment participant                
##  student_t(3, 0, 2.5)        sd         difficulty participant                
##  student_t(3, 0, 2.5)        sd          Intercept participant                
##  student_t(3, 0, 2.5)        sd           intimacy participant                
##  student_t(3, 0, 2.5)        sd other_contribution participant                
##  student_t(3, 0, 2.5)        sd       pleasantness participant                
##  student_t(3, 0, 2.5)        sd  self_contribution participant                
##  student_t(3, 0, 2.5)        sd                           word                
##  student_t(3, 0, 2.5)        sd          Intercept        word                
##  lb ub       source
##             default
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##             default
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##   0         default
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)

Check posterior predictive checks of the mixed beta regression:

pp_check(covariates_IOS_mdl, ndraws = 100, type = 'ecdf_overlay')

Check this model:

covariates_IOS_mdl
##  Family: cumulative 
##   Links: mu = logit; disc = identity 
## Formula: IOS ~ 1 + pleasantness + commitment + intimacy + difficulty + self_contribution + other_contribution + (1 | participant) + (0 + pleasantness | participant) + (0 + commitment | participant) + (0 + intimacy | participant) + (0 + difficulty | participant) + (0 + self_contribution | participant) + (0 + other_contribution | participant) + (1 | word) 
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept)              1.40      0.48     0.27     2.24 1.00     1197
## sd(pleasantness)           0.02      0.01     0.01     0.03 1.00     1945
## sd(commitment)             0.02      0.01     0.00     0.03 1.01     1172
## sd(intimacy)               0.02      0.01     0.00     0.03 1.00     1799
## sd(difficulty)             0.01      0.01     0.00     0.03 1.00     2022
## sd(self_contribution)      0.01      0.01     0.00     0.02 1.00     1941
## sd(other_contribution)     0.01      0.01     0.00     0.03 1.00     1513
##                        Tail_ESS
## sd(Intercept)              1275
## sd(pleasantness)           1568
## sd(commitment)             2683
## sd(intimacy)               2095
## sd(difficulty)             3102
## sd(self_contribution)      3978
## sd(other_contribution)     4313
## 
## ~word (Number of levels: 32) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.09      0.07     0.00     0.24 1.00     7830     6551
## 
## Population-Level Effects: 
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept[1]           0.79      0.60    -0.39     1.98 1.00    14619     9690
## Intercept[2]           4.93      0.62     3.74     6.16 1.00    12938    10156
## Intercept[3]           8.07      0.67     6.80     9.40 1.00    11378     9852
## Intercept[4]          10.63      0.72     9.26    12.07 1.00    10521     9623
## Intercept[5]          13.49      0.79    11.99    15.08 1.00     9927     9165
## pleasantness           0.09      0.01     0.08     0.11 1.00     9954     9549
## commitment             0.01      0.01    -0.01     0.02 1.00    11038     9419
## intimacy               0.01      0.00     0.00     0.02 1.00    16090     9585
## difficulty            -0.01      0.00    -0.02    -0.00 1.00    17458     9863
## self_contribution     -0.00      0.01    -0.02     0.01 1.00    11348     8346
## other_contribution     0.00      0.01    -0.01     0.01 1.00    15542     9568
## 
## Family Specific Parameters: 
##      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc     1.00      0.00     1.00     1.00   NA       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Test all hypotheses from the covariate model:

hypothesis(covariates_IOS_mdl, 'pleasantness > 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (pleasantness) > 0     0.09      0.01     0.08      0.1        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_IOS_mdl, 'commitment > 0')
## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (commitment) > 0     0.01      0.01        0     0.02        7.4      0.88
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_IOS_mdl, 'intimacy > 0')
## Hypothesis Tests for class b:
##       Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (intimacy) > 0     0.01         0        0     0.02       65.3      0.98    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_IOS_mdl, 'difficulty < 0')
## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty) < 0    -0.01         0    -0.02        0      72.17      0.99
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_IOS_mdl, 'self_contribution > 0')
## Hypothesis Tests for class b:
##                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contribution) > 0        0      0.01    -0.01     0.01       0.56
##   Post.Prob Star
## 1      0.36     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_IOS_mdl, 'other_contribution > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contribution) > 0        0      0.01    -0.01     0.01        1.5
##   Post.Prob Star
## 1       0.6     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Now closeness as a function of all covariates:

covariates_dist_mdl <- brm(bf(closeness_01 ~ 
                             
                                # Fixed effects:
                             
                                1 +
                                pleasantness +
                                commitment +
                                intimacy +
                                difficulty +
                                self_contribution +
                                other_contribution +
                             
                                # Random effects:
                               
                                (1|participant) +
                                (0 + pleasantness|participant) +
                                (0 + commitment|participant) +
                                (0 + intimacy|participant) +
                                (0 + difficulty|participant) +
                                (0 + self_contribution|participant) +
                                (0 + other_contribution|participant) +
                                (1|word),
                              
                              # Family-specific parameter (shape):
                              
                              phi ~ 1),
                           
                           # General stuff:

                           data = df,
                           family = Beta,

                           # MCMC settings:

                           init = 0, # doesn't converge otherwise
                           seed = 42,
                           cores = 4,
                           iter = 6000,
                           warmup = 3000,
                           control = list(adapt_delta = 0.90))

# Save model:

save(covariates_dist_mdl, file = '../models_E2/covariates_dist_mdl.Rdata')

Load:

load('../models_E2/covariates_dist_mdl.Rdata')

Show priors:

prior_summary(covariates_dist_mdl)
##                 prior     class               coef       group resp dpar nlpar
##                (flat)         b                                               
##                (flat)         b         commitment                            
##                (flat)         b         difficulty                            
##                (flat)         b           intimacy                            
##                (flat)         b other_contribution                            
##                (flat)         b       pleasantness                            
##                (flat)         b  self_contribution                            
##  student_t(3, 0, 2.5) Intercept                                               
##  student_t(3, 0, 2.5) Intercept                                      phi      
##  student_t(3, 0, 2.5)        sd                                               
##  student_t(3, 0, 2.5)        sd                    participant                
##  student_t(3, 0, 2.5)        sd         commitment participant                
##  student_t(3, 0, 2.5)        sd         difficulty participant                
##  student_t(3, 0, 2.5)        sd          Intercept participant                
##  student_t(3, 0, 2.5)        sd           intimacy participant                
##  student_t(3, 0, 2.5)        sd other_contribution participant                
##  student_t(3, 0, 2.5)        sd       pleasantness participant                
##  student_t(3, 0, 2.5)        sd  self_contribution participant                
##  student_t(3, 0, 2.5)        sd                           word                
##  student_t(3, 0, 2.5)        sd          Intercept        word                
##  lb ub       source
##             default
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##             default
##             default
##   0         default
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)

Check posterior predictive checks of the mixed beta regression:

pp_check(covariates_dist_mdl,
         ndraws = 100, type = 'ecdf_overlay')

Check this model:

covariates_dist_mdl
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.9 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: closeness_01 ~ 1 + pleasantness + commitment + intimacy + difficulty + self_contribution + other_contribution + (1 | participant) + (0 + pleasantness | participant) + (0 + commitment | participant) + (0 + intimacy | participant) + (0 + difficulty | participant) + (0 + self_contribution | participant) + (0 + other_contribution | participant) + (1 | word) 
##          phi ~ 1
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept)              0.79      0.10     0.60     1.00 1.00     3466
## sd(pleasantness)           0.01      0.00     0.01     0.01 1.00     3183
## sd(commitment)             0.01      0.00     0.01     0.01 1.00     3458
## sd(intimacy)               0.01      0.00     0.00     0.01 1.00     3923
## sd(difficulty)             0.01      0.00     0.00     0.01 1.00     3839
## sd(self_contribution)      0.00      0.00     0.00     0.00 1.00     4318
## sd(other_contribution)     0.01      0.00     0.00     0.01 1.00     1428
##                        Tail_ESS
## sd(Intercept)              6218
## sd(pleasantness)           5441
## sd(commitment)             6062
## sd(intimacy)               4986
## sd(difficulty)             5495
## sd(self_contribution)      6045
## sd(other_contribution)     1200
## 
## ~word (Number of levels: 32) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.02      0.02     0.00     0.06 1.00     5094     5573
## 
## Population-Level Effects: 
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept             -0.49      0.15    -0.79    -0.20 1.00    10118     9756
## phi_Intercept          3.65      0.07     3.52     3.78 1.00     2286     5174
## pleasantness           0.02      0.00     0.01     0.02 1.00     8577     9634
## commitment            -0.00      0.00    -0.00     0.00 1.00     8875     9373
## intimacy               0.00      0.00    -0.00     0.00 1.00     9734     9692
## difficulty            -0.00      0.00    -0.00    -0.00 1.00    12465    10832
## self_contribution      0.00      0.00    -0.00     0.00 1.00    10569     9290
## other_contribution     0.01      0.00     0.00     0.01 1.00     9479     9751
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Test all hypotheses from the covariate model:

hypothesis(covariates_dist_mdl, 'pleasantness > 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (pleasantness) > 0     0.02         0     0.01     0.02        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_dist_mdl, 'commitment > 0')
## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (commitment) > 0        0         0        0        0       0.36      0.26
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_dist_mdl, 'intimacy > 0')
## Hypothesis Tests for class b:
##       Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (intimacy) > 0        0         0        0        0       3.42      0.77     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_dist_mdl, 'difficulty < 0')
## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty) < 0        0         0        0        0      56.42      0.98
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_dist_mdl, 'self_contribution > 0')
## Hypothesis Tests for class b:
##                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contribution) > 0        0         0        0        0        1.9
##   Post.Prob Star
## 1      0.66     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(covariates_dist_mdl, 'other_contribution > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contribution) > 0     0.01         0        0     0.01        Inf
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

10 Difficulty analysis

As we are learning from the first experiment, this analysis already directly includes difficulty as a covariate. We’ll test the effect of difficulty on category anyway, and also on subclusters!

Make a graph of this.

# Plot core:

category_difficulty_p <- df %>% 
  ggplot(aes(x = difficulty, fill = category)) +
  geom_density(alpha = 0.55) +
  annotate(geom = 'text',
           label = 'concrete concepts',
           color = 'goldenrod3',
           x = 39, y = 0.011,
           hjust = 0, size = 4) +
  annotate(geom = 'text',
           label = 'abstract concepts',
           color = 'steelblue',
           x = 68, y = 0.0075,
           hjust = 0, size = 4)

# Scales and axes:

category_difficulty_p <- category_difficulty_p +
  scale_x_continuous(expand = c(0, 0),
                     limits = c(0, 100),
                     breaks = seq(0, 100, 25)) +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 0.02)) +
  scale_fill_manual(values = c('goldenrod3', 'steelblue')) +
  xlab('Difficulty') +
  ylab('Density')

# Cosmetics:

category_difficulty_p <- category_difficulty_p +
  theme_classic() +
  theme(legend.position = 'none',
        legend.title = element_blank(),
        axis.title = element_text(face = 'bold',
                                  size = 12.5),
        axis.title.x = element_text(margin = margin(t = 6.5)),
        axis.title.y = element_text(margin = margin(r = 10)))

# Show:

category_difficulty_p

ggsave('../figures_E2/category_difficulty_E2.pdf', plot = category_difficulty_p,
       width = 5, height = 3.5)

Since difficulty is now the dependent measure, convert it into [0, 1] for beta regression. We’re adding 0.001 to the zero cases here because otherwise we can’t run teh beta regression.

df <- mutate(df,
             difficulty_01 = difficulty / 100,
             difficulty_01 = ifelse(difficulty_01 == 0, 0.001, difficulty_01))

Model difficulty as a function of category with a beta regression model then:

difficulty_mdl <- brm(bf(difficulty_01 ~ 
                           
                           # Fixed effects:
                           
                           1 +
                           category +
                           
                           # Random effects:
                           
                           (1 + category|participant) +
                           (1|word),
                        
                         # Family-specific parameter (shape):
                        
                         phi ~ 1 + category),
           
                      data = df, # interactive only
                      family = Beta,
           
                      # MCMC settings:
           
                      seed = 42,
                      init = 0,
                      cores = 4,
                      iter = 6000,
                      warmup = 3000,
                      control = list(adapt_delta = 0.99))

# Save model:

save(difficulty_mdl, file = '../models_E2/difficulty_mdl.Rdata')

Load model:

load('../models_E2/difficulty_mdl.Rdata')

Show priors:

prior_summary(difficulty_mdl)
##                 prior     class             coef       group resp dpar nlpar lb
##                (flat)         b                                                
##                (flat)         b categoryabstract                               
##                (flat)         b                                    phi         
##                (flat)         b categoryabstract                   phi         
##  student_t(3, 0, 2.5) Intercept                                                
##  student_t(3, 0, 2.5) Intercept                                    phi         
##  lkj_corr_cholesky(1)         L                                                
##  lkj_corr_cholesky(1)         L                  participant                   
##  student_t(3, 0, 2.5)        sd                                               0
##  student_t(3, 0, 2.5)        sd                  participant                  0
##  student_t(3, 0, 2.5)        sd categoryabstract participant                  0
##  student_t(3, 0, 2.5)        sd        Intercept participant                  0
##  student_t(3, 0, 2.5)        sd                         word                  0
##  student_t(3, 0, 2.5)        sd        Intercept        word                  0
##  ub       source
##          default
##     (vectorized)
##          default
##     (vectorized)
##          default
##          default
##          default
##     (vectorized)
##          default
##     (vectorized)
##     (vectorized)
##     (vectorized)
##     (vectorized)
##     (vectorized)

Check posterior predictive checks of the mixed beta regression:

pp_check(difficulty_mdl, ndraws = 100)

Check this model:

difficulty_mdl
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: difficulty_01 ~ 1 + category + (1 + category | participant) + (1 | word) 
##          phi ~ 1 + category
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                 Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                       0.80      0.07     0.67     0.95 1.00
## sd(categoryabstract)                0.64      0.09     0.46     0.81 1.00
## cor(Intercept,categoryabstract)    -0.36      0.13    -0.59    -0.09 1.00
##                                 Bulk_ESS Tail_ESS
## sd(Intercept)                       4819     7275
## sd(categoryabstract)                2972     3568
## cor(Intercept,categoryabstract)     5526     7434
## 
## ~word (Number of levels: 32) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.07      0.05     0.00     0.17 1.00     3638     5474
## 
## Population-Level Effects: 
##                      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept               -0.91      0.08    -1.08    -0.74 1.00     4908
## phi_Intercept            1.45      0.07     1.32     1.59 1.00     8858
## categoryabstract         0.07      0.09    -0.11     0.24 1.00     8411
## phi_categoryabstract     0.01      0.10    -0.19     0.20 1.00    12204
##                      Tail_ESS
## Intercept                7000
## phi_Intercept            8930
## categoryabstract         9773
## phi_categoryabstract     9624
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis test on the category fixed effects coefficient:

hypothesis(difficulty_mdl, 'categoryabstract > 0')
## Hypothesis Tests for class b:
##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) > 0     0.07      0.09    -0.08     0.21       3.71
##   Post.Prob Star
## 1      0.79     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Model difficulty as a function of subcluster with a beta regression model then:

diff_subcluster_mdl <- brm(bf(difficulty_01 ~ 
                                
                                # Fixed effects:
                                
                                1 +
                                subcluster +
                           
                                # Random effects:
                           
                                (1 + subcluster|participant) +
                                (1|word),
                        
                              # Family-specific parameter (shape):
                        
                              phi ~ 1),
           
                           data = df, # interactive only
                           family = Beta,
           
                           # MCMC settings:
           
                           seed = 42,
                           init = 0,
                           cores = 4,
                           iter = 6000,
                           warmup = 3000,
                           control = list(adapt_delta = 0.99))

# Save model:

save(diff_subcluster_mdl,
     file = '../models_E2/difficulty_subcluster_mdl.Rdata')

Load model:

load('../models_E2/difficulty_subcluster_mdl.Rdata')

Show priors:

prior_summary(diff_subcluster_mdl)
##                 prior     class              coef       group resp dpar nlpar
##                (flat)         b                                              
##                (flat)         b subclusterConc_an                            
##                (flat)         b subclusterConc_in                            
##                (flat)         b      subclusterEM                            
##                (flat)         b      subclusterPS                            
##                (flat)         b      subclusterSS                            
##  student_t(3, 0, 2.5) Intercept                                              
##  student_t(3, 0, 2.5) Intercept                                     phi      
##  lkj_corr_cholesky(1)         L                                              
##  lkj_corr_cholesky(1)         L                   participant                
##  student_t(3, 0, 2.5)        sd                                              
##  student_t(3, 0, 2.5)        sd                   participant                
##  student_t(3, 0, 2.5)        sd         Intercept participant                
##  student_t(3, 0, 2.5)        sd subclusterConc_an participant                
##  student_t(3, 0, 2.5)        sd subclusterConc_in participant                
##  student_t(3, 0, 2.5)        sd      subclusterEM participant                
##  student_t(3, 0, 2.5)        sd      subclusterPS participant                
##  student_t(3, 0, 2.5)        sd      subclusterSS participant                
##  student_t(3, 0, 2.5)        sd                          word                
##  student_t(3, 0, 2.5)        sd         Intercept        word                
##  lb ub       source
##             default
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##        (vectorized)
##             default
##             default
##             default
##        (vectorized)
##   0         default
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)
##   0    (vectorized)

Check posterior predictive checks of the mixed beta regression:

pp_check(diff_subcluster_mdl, ndraws = 100)

Check this model:

diff_subcluster_mdl
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: difficulty_01 ~ 1 + subcluster + (1 + subcluster | participant) + (1 | word) 
##          phi ~ 1
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                          Estimate Est.Error l-95% CI u-95% CI
## sd(Intercept)                                0.80      0.08     0.66     0.96
## sd(subclusterConc_an)                        0.63      0.12     0.40     0.87
## sd(subclusterConc_in)                        0.57      0.12     0.33     0.80
## sd(subclusterEM)                             0.13      0.09     0.01     0.34
## sd(subclusterPS)                             0.38      0.20     0.03     0.74
## sd(subclusterSS)                             0.23      0.16     0.01     0.59
## cor(Intercept,subclusterConc_an)            -0.32      0.15    -0.58    -0.00
## cor(Intercept,subclusterConc_in)            -0.27      0.17    -0.56     0.09
## cor(subclusterConc_an,subclusterConc_in)     0.84      0.10     0.58     0.97
## cor(Intercept,subclusterEM)                 -0.03      0.36    -0.68     0.67
## cor(subclusterConc_an,subclusterEM)          0.22      0.38    -0.59     0.83
## cor(subclusterConc_in,subclusterEM)          0.20      0.38    -0.58     0.81
## cor(Intercept,subclusterPS)                  0.05      0.27    -0.47     0.61
## cor(subclusterConc_an,subclusterPS)         -0.17      0.30    -0.73     0.45
## cor(subclusterConc_in,subclusterPS)         -0.20      0.31    -0.76     0.43
## cor(subclusterEM,subclusterPS)               0.04      0.37    -0.67     0.72
## cor(Intercept,subclusterSS)                  0.03      0.34    -0.62     0.67
## cor(subclusterConc_an,subclusterSS)         -0.14      0.35    -0.75     0.59
## cor(subclusterConc_in,subclusterSS)         -0.06      0.35    -0.70     0.63
## cor(subclusterEM,subclusterSS)               0.02      0.38    -0.70     0.71
## cor(subclusterPS,subclusterSS)              -0.07      0.36    -0.73     0.66
##                                          Rhat Bulk_ESS Tail_ESS
## sd(Intercept)                            1.00     5613     8177
## sd(subclusterConc_an)                    1.00     2519     2696
## sd(subclusterConc_in)                    1.00     2462     2599
## sd(subclusterEM)                         1.00     4782     6866
## sd(subclusterPS)                         1.00     1859     3702
## sd(subclusterSS)                         1.00     3083     5538
## cor(Intercept,subclusterConc_an)         1.00     6903     6238
## cor(Intercept,subclusterConc_in)         1.00     6896     6271
## cor(subclusterConc_an,subclusterConc_in) 1.00     4286     5245
## cor(Intercept,subclusterEM)              1.00    23371     9032
## cor(subclusterConc_an,subclusterEM)      1.00     9727     9454
## cor(subclusterConc_in,subclusterEM)      1.00     9104     9359
## cor(Intercept,subclusterPS)              1.00    13260     7111
## cor(subclusterConc_an,subclusterPS)      1.00     5943     8008
## cor(subclusterConc_in,subclusterPS)      1.00     6323     8785
## cor(subclusterEM,subclusterPS)           1.00     4300     7288
## cor(Intercept,subclusterSS)              1.00    19394     8511
## cor(subclusterConc_an,subclusterSS)      1.00    11677     9111
## cor(subclusterConc_in,subclusterSS)      1.00    12842     9681
## cor(subclusterEM,subclusterSS)           1.00     9320    10741
## cor(subclusterPS,subclusterSS)           1.00     9564    10460
## 
## ~word (Number of levels: 32) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.10      0.05     0.01     0.21 1.00     3198     5584
## 
## Population-Level Effects: 
##                   Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            -0.89      0.12    -1.13    -0.65 1.00     7021     8360
## phi_Intercept         1.50      0.06     1.38     1.62 1.00     3583     6923
## subclusterConc_an    -0.03      0.13    -0.29     0.24 1.00     9299     8963
## subclusterConc_in    -0.04      0.13    -0.30     0.22 1.00     9631     9182
## subclusterEM          0.04      0.13    -0.22     0.30 1.00    10297     8970
## subclusterPS          0.11      0.14    -0.17     0.40 1.00    11618    10169
## subclusterSS         -0.03      0.15    -0.33     0.27 1.00    12011    10029
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis test on the subcluster fixed effects coefficient:

# ...

11 Category analysis: other-contribution

Do the main analysis of IOS with difficulty as a covariate predictor, to control for this.

IOS_category_mdl <- brm(IOS ~ 
                          
                          # Fixed effects:
                                 
                          1 +
                          category +
                          other_contribution_c +
                          difficulty_c +
                          category:other_contribution_c +
                          
                          # Random effects:
                                 
                          (1 +
                             category +
                             other_contribution_c +
                             category:other_contribution_c|participant) +
                          (1 + other_contribution_c|word),
           
                        data = df,
                        family = cumulative,
           
                        # MCMC settings:
                               
                        seed = 42,
                        cores = 4,
                        iter = 6000,
                        warmup = 3000,
                        save_pars = save_pars(all = TRUE), # for bayes factors
                        control = list(adapt_delta = 0.99))

# Save model:

save(IOS_category_mdl,
     file = '../models_E2/IOS_category_mdl.Rdata')

Corresponding null model:

IOS_category_null <- brm(IOS ~ 
                                 
                           # Fixed effects:
                           
                           1 +
                           category +
                           other_contribution_c +
                           difficulty_c +
                                 
                           # Random effects:
                                 
                           (1 +
                              category +
                              other_contribution_c +
                              category:other_contribution_c|participant) +
                           (1 + other_contribution_c|word),
           
                         data = df,
                         family = cumulative,
           
                         # MCMC settings:
                               
                         seed = 42,
                         cores = 4,
                         iter = 6000,
                         warmup = 3000,
                         save_pars = save_pars(all = TRUE), # for bayes factor
                         control = list(adapt_delta = 0.99))

# Save model:

save(IOS_category_null,
     file = '../models_E2/IOS_category_null.Rdata')

Load model:

load('../models_E2/IOS_category_mdl.Rdata')
load('../models_E2/IOS_category_null.Rdata')

Show priors:

prior_summary(IOS_category_mdl)
##                 prior     class                                  coef
##                (flat)         b                                      
##                (flat)         b                      categoryabstract
##                (flat)         b categoryabstract:other_contribution_c
##                (flat)         b                          difficulty_c
##                (flat)         b                  other_contribution_c
##  student_t(3, 0, 2.5) Intercept                                      
##  student_t(3, 0, 2.5) Intercept                                     1
##  student_t(3, 0, 2.5) Intercept                                     2
##  student_t(3, 0, 2.5) Intercept                                     3
##  student_t(3, 0, 2.5) Intercept                                     4
##  student_t(3, 0, 2.5) Intercept                                     5
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                      categoryabstract
##  student_t(3, 0, 2.5)        sd categoryabstract:other_contribution_c
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                  other_contribution_c
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                  other_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
prior_summary(IOS_category_null)
##                 prior     class                                  coef
##                (flat)         b                                      
##                (flat)         b                      categoryabstract
##                (flat)         b                          difficulty_c
##                (flat)         b                  other_contribution_c
##  student_t(3, 0, 2.5) Intercept                                      
##  student_t(3, 0, 2.5) Intercept                                     1
##  student_t(3, 0, 2.5) Intercept                                     2
##  student_t(3, 0, 2.5) Intercept                                     3
##  student_t(3, 0, 2.5) Intercept                                     4
##  student_t(3, 0, 2.5) Intercept                                     5
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                      categoryabstract
##  student_t(3, 0, 2.5)        sd categoryabstract:other_contribution_c
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                  other_contribution_c
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                  other_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)

Bayes factors for both:

# Compute:

IOS_bf <- bayes_factor(IOS_category_mdl, IOS_category_null)

# Save:

save(IOS_bf,
     file = '../models_E2/IOS_bf.RData')

Show Bayes factor:

# Load:

load('../models_E2/IOS_bf.RData')

# Show:

IOS_bf
## Estimated Bayes factor in favor of IOS_category_mdl over IOS_category_null: 0.07764

Compute R-squared:

bayes_R2(IOS_category_mdl)
## Warning: Predictions are treated as continuous variables in 'bayes_R2' which is
## likely invalid for ordinal families.
##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.7081655 0.01295892 0.6811916 0.7317703
bayes_R2(IOS_category_null)
## Warning: Predictions are treated as continuous variables in 'bayes_R2' which is
## likely invalid for ordinal families.
##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.7086503 0.01252542 0.6828421 0.7315246
# Check:

0.7081655 - 0.7086503
## [1] -0.0004848

The model with the interaction is nearly equivalent in R-squared to the model without the interaction.

Check posterior predictive checks of the mixed beta regression:

pp_check(IOS_category_mdl, ndraws = 100)

Check this model:

IOS_category_mdl
##  Family: cumulative 
##   Links: mu = logit; disc = identity 
## Formula: IOS ~ 1 + category + other_contribution_c + difficulty_c + category:other_contribution_c + (1 + category + other_contribution_c + category:other_contribution_c | participant) + (1 + other_contribution_c | word) 
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                 Estimate
## sd(Intercept)                                                       2.80
## sd(categoryabstract)                                                1.58
## sd(other_contribution_c)                                            0.06
## sd(categoryabstract:other_contribution_c)                           0.06
## cor(Intercept,categoryabstract)                                    -0.34
## cor(Intercept,other_contribution_c)                                 0.13
## cor(categoryabstract,other_contribution_c)                          0.03
## cor(Intercept,categoryabstract:other_contribution_c)               -0.11
## cor(categoryabstract,categoryabstract:other_contribution_c)        -0.03
## cor(other_contribution_c,categoryabstract:other_contribution_c)    -0.54
##                                                                 Est.Error
## sd(Intercept)                                                        0.25
## sd(categoryabstract)                                                 0.29
## sd(other_contribution_c)                                             0.01
## sd(categoryabstract:other_contribution_c)                            0.02
## cor(Intercept,categoryabstract)                                      0.14
## cor(Intercept,other_contribution_c)                                  0.16
## cor(categoryabstract,other_contribution_c)                           0.22
## cor(Intercept,categoryabstract:other_contribution_c)                 0.20
## cor(categoryabstract,categoryabstract:other_contribution_c)          0.26
## cor(other_contribution_c,categoryabstract:other_contribution_c)      0.27
##                                                                 l-95% CI
## sd(Intercept)                                                       2.33
## sd(categoryabstract)                                                1.00
## sd(other_contribution_c)                                            0.04
## sd(categoryabstract:other_contribution_c)                           0.01
## cor(Intercept,categoryabstract)                                    -0.57
## cor(Intercept,other_contribution_c)                                -0.19
## cor(categoryabstract,other_contribution_c)                         -0.40
## cor(Intercept,categoryabstract:other_contribution_c)               -0.52
## cor(categoryabstract,categoryabstract:other_contribution_c)        -0.48
## cor(other_contribution_c,categoryabstract:other_contribution_c)    -0.86
##                                                                 u-95% CI Rhat
## sd(Intercept)                                                       3.33 1.00
## sd(categoryabstract)                                                2.14 1.00
## sd(other_contribution_c)                                            0.09 1.01
## sd(categoryabstract:other_contribution_c)                           0.10 1.01
## cor(Intercept,categoryabstract)                                    -0.05 1.00
## cor(Intercept,other_contribution_c)                                 0.43 1.00
## cor(categoryabstract,other_contribution_c)                          0.45 1.01
## cor(Intercept,categoryabstract:other_contribution_c)                0.27 1.00
## cor(categoryabstract,categoryabstract:other_contribution_c)         0.56 1.00
## cor(other_contribution_c,categoryabstract:other_contribution_c)     0.22 1.00
##                                                                 Bulk_ESS
## sd(Intercept)                                                       2547
## sd(categoryabstract)                                                1101
## sd(other_contribution_c)                                             805
## sd(categoryabstract:other_contribution_c)                            435
## cor(Intercept,categoryabstract)                                     3174
## cor(Intercept,other_contribution_c)                                 5028
## cor(categoryabstract,other_contribution_c)                          1367
## cor(Intercept,categoryabstract:other_contribution_c)                5323
## cor(categoryabstract,categoryabstract:other_contribution_c)         1432
## cor(other_contribution_c,categoryabstract:other_contribution_c)      866
##                                                                 Tail_ESS
## sd(Intercept)                                                       5018
## sd(categoryabstract)                                                1369
## sd(other_contribution_c)                                            2128
## sd(categoryabstract:other_contribution_c)                            597
## cor(Intercept,categoryabstract)                                     3755
## cor(Intercept,other_contribution_c)                                 6635
## cor(categoryabstract,other_contribution_c)                          2430
## cor(Intercept,categoryabstract:other_contribution_c)                2966
## cor(categoryabstract,categoryabstract:other_contribution_c)         1471
## cor(other_contribution_c,categoryabstract:other_contribution_c)      971
## 
## ~word (Number of levels: 32) 
##                                     Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                           0.09      0.07     0.00     0.26 1.00
## sd(other_contribution_c)                0.01      0.01     0.00     0.02 1.00
## cor(Intercept,other_contribution_c)     0.01      0.58    -0.95     0.96 1.00
##                                     Bulk_ESS Tail_ESS
## sd(Intercept)                           6987     5823
## sd(other_contribution_c)                4197     5680
## cor(Intercept,other_contribution_c)     6166     7073
## 
## Population-Level Effects: 
##                                       Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1]                             -5.60      0.37    -6.32    -4.90 1.00
## Intercept[2]                             -1.86      0.29    -2.44    -1.29 1.00
## Intercept[3]                              0.93      0.29     0.37     1.50 1.00
## Intercept[4]                              3.26      0.32     2.65     3.89 1.00
## Intercept[5]                              5.96      0.39     5.21     6.75 1.00
## categoryabstract                          0.02      0.22    -0.40     0.45 1.00
## other_contribution_c                      0.06      0.01     0.04     0.08 1.00
## difficulty_c                             -0.03      0.00    -0.04    -0.02 1.00
## categoryabstract:other_contribution_c     0.00      0.01    -0.02     0.03 1.00
##                                       Bulk_ESS Tail_ESS
## Intercept[1]                              3186     6206
## Intercept[2]                              2808     5001
## Intercept[3]                              2817     4706
## Intercept[4]                              3047     5276
## Intercept[5]                              3284     6077
## categoryabstract                          6039     8332
## other_contribution_c                      3773     6786
## difficulty_c                             10301     9445
## categoryabstract:other_contribution_c     6117     7567
## 
## Family Specific Parameters: 
##      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc     1.00      0.00     1.00     1.00   NA       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(IOS_category_mdl,
           'categoryabstract < 0')
## Hypothesis Tests for class b:
##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) < 0     0.02      0.22    -0.33     0.38       0.83
##   Post.Prob Star
## 1      0.45     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_category_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.03         0    -0.04    -0.03        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_category_mdl,
           'other_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0     0.06      0.01     0.04     0.08        Inf
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_category_mdl,
           'categoryabstract:other_contribution_c  > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract... > 0        0      0.01    -0.02     0.02       1.73
##   Post.Prob Star
## 1      0.63     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Re-do the other main model, the one with closeness_01 as dependent variable, this time also with a difficulty_c control covariate:

dist_mdl <- brm(bf(closeness_01 ~ 
                     
                     # Fixed effects:
                                      
                     1 +
                     category +
                     other_contribution_c +
                     difficulty_c +
                     category:other_contribution_c +
                                      
                     # Random effects:
                                      
                     (1 +
                        category +
                        other_contribution_c +
                        category:other_contribution_c|participant) +
                     (1 + other_contribution_c|word),
                   phi ~ 1 + category),
           
                data = df, # interactive only
                family = Beta,
           
                # MCMC settings:
           
                seed = 42,
                init = 0,
                cores = 4,
                iter = 7500,
                warmup = 3500,
                save_pars = save_pars(all = TRUE), # for bayes factor
                control = list(adapt_delta = 0.99))

# Save model:

save(dist_mdl,
     file = '../models_E2/dist_mdl.Rdata')

Corresponding null model:

dist_null_mdl <- brm(bf(closeness_01 ~ 
                                      
                          # Fixed effects:
                                      
                          1 +
                          category +
                          other_contribution_c +
                          difficulty_c +
                                      
                          # Random effects:
                                      
                          (1 +
                             category +
                             other_contribution_c +
                             category:other_contribution_c|participant) +
                          (1 + other_contribution_c|word),
                        phi ~ 1 + category),
           
                     data = df, # interactive only
                     family = Beta,
           
                     # MCMC settings:
           
                     seed = 42,
                     init = 0,
                     cores = 4,
                     iter = 7500,
                     warmup = 3500,
                     save_pars = save_pars(all = TRUE), # for bayes factor
                     control = list(adapt_delta = 0.99))

# Save model:

save(dist_null_mdl,
     file = '../models_E2/dist_null_mdl.Rdata')

Load model:

load('../models_E2/dist_mdl.Rdata')
load('../models_E2/dist_null_mdl.Rdata')

Show priors:

prior_summary(dist_mdl)
##                 prior     class                                  coef
##                (flat)         b                                      
##                (flat)         b                      categoryabstract
##                (flat)         b categoryabstract:other_contribution_c
##                (flat)         b                          difficulty_c
##                (flat)         b                  other_contribution_c
##                (flat)         b                                      
##                (flat)         b                      categoryabstract
##  student_t(3, 0, 2.5) Intercept                                      
##  student_t(3, 0, 2.5) Intercept                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                      categoryabstract
##  student_t(3, 0, 2.5)        sd categoryabstract:other_contribution_c
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                  other_contribution_c
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                  other_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                    phi                  default
##                    phi             (vectorized)
##                                         default
##                    phi                  default
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
prior_summary(dist_null_mdl)
##                 prior     class                                  coef
##                (flat)         b                                      
##                (flat)         b                      categoryabstract
##                (flat)         b                          difficulty_c
##                (flat)         b                  other_contribution_c
##                (flat)         b                                      
##                (flat)         b                      categoryabstract
##  student_t(3, 0, 2.5) Intercept                                      
##  student_t(3, 0, 2.5) Intercept                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                      categoryabstract
##  student_t(3, 0, 2.5)        sd categoryabstract:other_contribution_c
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                  other_contribution_c
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                  other_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                    phi                  default
##                    phi             (vectorized)
##                                         default
##                    phi                  default
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)

Bayes factors for both:

# Compute:

dist_bf <- bayes_factor(dist_mdl, dist_null_mdl)

# Save:

save(dist_bf,
     file = '../models_E2/dist_bf.RData')

Show Bayes factor:

# Load:

load('../models_E2/dist_bf.RData')

# Show:

dist_bf
## Estimated Bayes factor in favor of dist_mdl over dist_null_mdl: 0.17835

Check posterior predictive checks of the mixed beta regression:

pp_check(dist_mdl, ndraws = 100)

Check this model:

dist_mdl
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: closeness_01 ~ 1 + category + other_contribution_c + difficulty_c + category:other_contribution_c + (1 + category + other_contribution_c + category:other_contribution_c | participant) + (1 + other_contribution_c | word) 
##          phi ~ 1 + category
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 7500; warmup = 3500; thin = 1;
##          total post-warmup draws = 16000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                 Estimate
## sd(Intercept)                                                       0.91
## sd(categoryabstract)                                                0.50
## sd(other_contribution_c)                                            0.02
## sd(categoryabstract:other_contribution_c)                           0.02
## cor(Intercept,categoryabstract)                                    -0.39
## cor(Intercept,other_contribution_c)                                 0.08
## cor(categoryabstract,other_contribution_c)                         -0.20
## cor(Intercept,categoryabstract:other_contribution_c)               -0.05
## cor(categoryabstract,categoryabstract:other_contribution_c)        -0.11
## cor(other_contribution_c,categoryabstract:other_contribution_c)    -0.13
##                                                                 Est.Error
## sd(Intercept)                                                        0.06
## sd(categoryabstract)                                                 0.09
## sd(other_contribution_c)                                             0.00
## sd(categoryabstract:other_contribution_c)                            0.00
## cor(Intercept,categoryabstract)                                      0.11
## cor(Intercept,other_contribution_c)                                  0.14
## cor(categoryabstract,other_contribution_c)                           0.19
## cor(Intercept,categoryabstract:other_contribution_c)                 0.16
## cor(categoryabstract,categoryabstract:other_contribution_c)          0.18
## cor(other_contribution_c,categoryabstract:other_contribution_c)      0.27
##                                                                 l-95% CI
## sd(Intercept)                                                       0.79
## sd(categoryabstract)                                                0.31
## sd(other_contribution_c)                                            0.01
## sd(categoryabstract:other_contribution_c)                           0.01
## cor(Intercept,categoryabstract)                                    -0.59
## cor(Intercept,other_contribution_c)                                -0.20
## cor(categoryabstract,other_contribution_c)                         -0.55
## cor(Intercept,categoryabstract:other_contribution_c)               -0.37
## cor(categoryabstract,categoryabstract:other_contribution_c)        -0.45
## cor(other_contribution_c,categoryabstract:other_contribution_c)    -0.57
##                                                                 u-95% CI Rhat
## sd(Intercept)                                                       1.05 1.00
## sd(categoryabstract)                                                0.68 1.00
## sd(other_contribution_c)                                            0.02 1.00
## sd(categoryabstract:other_contribution_c)                           0.03 1.00
## cor(Intercept,categoryabstract)                                    -0.15 1.00
## cor(Intercept,other_contribution_c)                                 0.37 1.00
## cor(categoryabstract,other_contribution_c)                          0.19 1.00
## cor(Intercept,categoryabstract:other_contribution_c)                0.26 1.00
## cor(categoryabstract,categoryabstract:other_contribution_c)         0.25 1.00
## cor(other_contribution_c,categoryabstract:other_contribution_c)     0.48 1.00
##                                                                 Bulk_ESS
## sd(Intercept)                                                       3907
## sd(categoryabstract)                                                1584
## sd(other_contribution_c)                                            2687
## sd(categoryabstract:other_contribution_c)                           1702
## cor(Intercept,categoryabstract)                                     7223
## cor(Intercept,other_contribution_c)                                 7786
## cor(categoryabstract,other_contribution_c)                          2170
## cor(Intercept,categoryabstract:other_contribution_c)                9692
## cor(categoryabstract,categoryabstract:other_contribution_c)         5147
## cor(other_contribution_c,categoryabstract:other_contribution_c)     1510
##                                                                 Tail_ESS
## sd(Intercept)                                                       6903
## sd(categoryabstract)                                                2092
## sd(other_contribution_c)                                            5945
## sd(categoryabstract:other_contribution_c)                           2945
## cor(Intercept,categoryabstract)                                     9980
## cor(Intercept,other_contribution_c)                                10675
## cor(categoryabstract,other_contribution_c)                          3359
## cor(Intercept,categoryabstract:other_contribution_c)               10497
## cor(categoryabstract,categoryabstract:other_contribution_c)         8205
## cor(other_contribution_c,categoryabstract:other_contribution_c)     2791
## 
## ~word (Number of levels: 32) 
##                                     Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                           0.04      0.03     0.00     0.10 1.00
## sd(other_contribution_c)                0.00      0.00     0.00     0.00 1.00
## cor(Intercept,other_contribution_c)     0.00      0.56    -0.94     0.94 1.00
##                                     Bulk_ESS Tail_ESS
## sd(Intercept)                           4513     6859
## sd(other_contribution_c)                5232     7474
## cor(Intercept,other_contribution_c)    10453    10039
## 
## Population-Level Effects: 
##                                       Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept                                 0.95      0.09     0.78     1.12 1.00
## phi_Intercept                             3.58      0.08     3.42     3.73 1.00
## categoryabstract                         -0.03      0.06    -0.15     0.10 1.00
## other_contribution_c                      0.02      0.00     0.01     0.02 1.00
## difficulty_c                             -0.01      0.00    -0.01    -0.00 1.00
## categoryabstract:other_contribution_c    -0.00      0.00    -0.01     0.00 1.00
## phi_categoryabstract                     -0.33      0.13    -0.58    -0.08 1.00
##                                       Bulk_ESS Tail_ESS
## Intercept                                 2311     4677
## phi_Intercept                            11617    12038
## categoryabstract                          8504    10700
## other_contribution_c                      9558    10827
## difficulty_c                             18767    14975
## categoryabstract:other_contribution_c    11433    12172
## phi_categoryabstract                      5046     9603
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(dist_mdl,
           'categoryabstract > 0')
## Hypothesis Tests for class b:
##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) > 0    -0.03      0.06    -0.13     0.08        0.5
##   Post.Prob Star
## 1      0.33     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.01         0    -0.01        0        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_mdl,
           'other_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0     0.02         0     0.01     0.02        Inf
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_mdl,
           'categoryabstract:other_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract... > 0        0         0    -0.01        0       0.45
##   Post.Prob Star
## 1      0.31     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

12 Category analysis: self-contribution

A repeat of the main analysis, but this time testing the interaction with other_contribution rather than self_contribution.

IOS_self_mdl <- brm(IOS ~ 
                      
                      # Fixed effects:
                           
                      1 +
                      category +
                      self_contribution_c +
                      difficulty_c +
                      category:self_contribution_c +
                                 
                      # Random effects:
                                 
                      (1 +
                         category +
                         self_contribution_c +
                         category:self_contribution_c|participant) +
                      (1 + self_contribution_c|word),
           
                    data = df,
                    family = cumulative,
           
                    # MCMC settings:
                               
                    seed = 42,
                    cores = 4,
                    iter = 6000,
                    warmup = 3000,
                    save_pars = save_pars(all = TRUE), # for bayes factors
                    control = list(adapt_delta = 0.99))

# Save model:

save(IOS_self_mdl,
     file = '../models_E2/IOS_self_mdl.Rdata')

Fit the corresponding null model:

IOS_self_null <- brm(IOS ~ 
                      
                      # Fixed effects:
                           
                      1 +
                      category +
                      self_contribution_c +
                      difficulty_c +
                                 
                      # Random effects:
                                 
                      (1 +
                         category +
                         self_contribution_c +
                         category:self_contribution_c|participant) +
                      (1 + self_contribution_c|word),
           
                    data = df,
                    family = cumulative,
           
                    # MCMC settings:
                               
                    seed = 42,
                    cores = 4,
                    iter = 6000,
                    warmup = 3000,
                    save_pars = save_pars(all = TRUE), # for bayes factors
                    control = list(adapt_delta = 0.99))

# Save model:

save(IOS_null_mdl,
     file = '../models_E2/IOS_self_null.Rdata')

Load model:

load('../models_E2/IOS_self_mdl.RData')
load('../models_E2/IOS_self_null.RData')

Show priors:

prior_summary(IOS_self_mdl)
##                 prior     class                                 coef
##                (flat)         b                                     
##                (flat)         b                     categoryabstract
##                (flat)         b categoryabstract:self_contribution_c
##                (flat)         b                         difficulty_c
##                (flat)         b                  self_contribution_c
##  student_t(3, 0, 2.5) Intercept                                     
##  student_t(3, 0, 2.5) Intercept                                    1
##  student_t(3, 0, 2.5) Intercept                                    2
##  student_t(3, 0, 2.5) Intercept                                    3
##  student_t(3, 0, 2.5) Intercept                                    4
##  student_t(3, 0, 2.5) Intercept                                    5
##  lkj_corr_cholesky(1)         L                                     
##  lkj_corr_cholesky(1)         L                                     
##  lkj_corr_cholesky(1)         L                                     
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                     categoryabstract
##  student_t(3, 0, 2.5)        sd categoryabstract:self_contribution_c
##  student_t(3, 0, 2.5)        sd                            Intercept
##  student_t(3, 0, 2.5)        sd                  self_contribution_c
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                            Intercept
##  student_t(3, 0, 2.5)        sd                  self_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
prior_summary(IOS_self_null)
##                 prior     class                                 coef
##                (flat)         b                                     
##                (flat)         b                     categoryabstract
##                (flat)         b                         difficulty_c
##                (flat)         b                  self_contribution_c
##  student_t(3, 0, 2.5) Intercept                                     
##  student_t(3, 0, 2.5) Intercept                                    1
##  student_t(3, 0, 2.5) Intercept                                    2
##  student_t(3, 0, 2.5) Intercept                                    3
##  student_t(3, 0, 2.5) Intercept                                    4
##  student_t(3, 0, 2.5) Intercept                                    5
##  lkj_corr_cholesky(1)         L                                     
##  lkj_corr_cholesky(1)         L                                     
##  lkj_corr_cholesky(1)         L                                     
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                     categoryabstract
##  student_t(3, 0, 2.5)        sd categoryabstract:self_contribution_c
##  student_t(3, 0, 2.5)        sd                            Intercept
##  student_t(3, 0, 2.5)        sd                  self_contribution_c
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                            Intercept
##  student_t(3, 0, 2.5)        sd                  self_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)

Bayes factors for both:

# Compute:

IOS_self_bf <- bayes_factor(IOS_self_mdl, IOS_self_null)

# Save:

save(IOS_self_bf,
     file = '../models_E2/IOS_self_bf.RData')

Show Bayes factor:

# Load:

load('../models_E2/IOS_self_bf.RData')

# Show:

dist_bf
## Estimated Bayes factor in favor of dist_mdl over dist_null_mdl: 0.17835

Check posterior predictive checks of the mixed beta regression:

pp_check(IOS_self_mdl, ndraws = 100)

Check this model:

IOS_self_mdl
##  Family: cumulative 
##   Links: mu = logit; disc = identity 
## Formula: IOS ~ 1 + category + self_contribution_c + difficulty_c + category:self_contribution_c + (1 + category + self_contribution_c + category:self_contribution_c | participant) + (1 + self_contribution_c | word) 
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                               Estimate
## sd(Intercept)                                                     2.83
## sd(categoryabstract)                                              1.86
## sd(self_contribution_c)                                           0.06
## sd(categoryabstract:self_contribution_c)                          0.03
## cor(Intercept,categoryabstract)                                  -0.36
## cor(Intercept,self_contribution_c)                                0.20
## cor(categoryabstract,self_contribution_c)                         0.21
## cor(Intercept,categoryabstract:self_contribution_c)              -0.33
## cor(categoryabstract,categoryabstract:self_contribution_c)        0.25
## cor(self_contribution_c,categoryabstract:self_contribution_c)    -0.36
##                                                               Est.Error
## sd(Intercept)                                                      0.25
## sd(categoryabstract)                                               0.24
## sd(self_contribution_c)                                            0.01
## sd(categoryabstract:self_contribution_c)                           0.02
## cor(Intercept,categoryabstract)                                    0.11
## cor(Intercept,self_contribution_c)                                 0.17
## cor(categoryabstract,self_contribution_c)                          0.20
## cor(Intercept,categoryabstract:self_contribution_c)                0.32
## cor(categoryabstract,categoryabstract:self_contribution_c)         0.31
## cor(self_contribution_c,categoryabstract:self_contribution_c)      0.39
##                                                               l-95% CI u-95% CI
## sd(Intercept)                                                     2.37     3.36
## sd(categoryabstract)                                              1.38     2.35
## sd(self_contribution_c)                                           0.03     0.09
## sd(categoryabstract:self_contribution_c)                          0.00     0.07
## cor(Intercept,categoryabstract)                                  -0.56    -0.12
## cor(Intercept,self_contribution_c)                               -0.15     0.53
## cor(categoryabstract,self_contribution_c)                        -0.19     0.60
## cor(Intercept,categoryabstract:self_contribution_c)              -0.86     0.40
## cor(categoryabstract,categoryabstract:self_contribution_c)       -0.44     0.80
## cor(self_contribution_c,categoryabstract:self_contribution_c)    -0.88     0.57
##                                                               Rhat Bulk_ESS
## sd(Intercept)                                                 1.00     3480
## sd(categoryabstract)                                          1.00     2484
## sd(self_contribution_c)                                       1.00     1495
## sd(categoryabstract:self_contribution_c)                      1.00      953
## cor(Intercept,categoryabstract)                               1.00     3640
## cor(Intercept,self_contribution_c)                            1.00     5636
## cor(categoryabstract,self_contribution_c)                     1.00     3001
## cor(Intercept,categoryabstract:self_contribution_c)           1.00     6886
## cor(categoryabstract,categoryabstract:self_contribution_c)    1.00     7058
## cor(self_contribution_c,categoryabstract:self_contribution_c) 1.00     1680
##                                                               Tail_ESS
## sd(Intercept)                                                     5591
## sd(categoryabstract)                                              3630
## sd(self_contribution_c)                                           3352
## sd(categoryabstract:self_contribution_c)                          2509
## cor(Intercept,categoryabstract)                                   5889
## cor(Intercept,self_contribution_c)                                7059
## cor(categoryabstract,self_contribution_c)                         4470
## cor(Intercept,categoryabstract:self_contribution_c)               5555
## cor(categoryabstract,categoryabstract:self_contribution_c)        6983
## cor(self_contribution_c,categoryabstract:self_contribution_c)     6376
## 
## ~word (Number of levels: 32) 
##                                    Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                          0.10      0.08     0.00     0.28 1.00
## sd(self_contribution_c)                0.01      0.01     0.00     0.02 1.00
## cor(Intercept,self_contribution_c)     0.17      0.57    -0.92     0.97 1.00
##                                    Bulk_ESS Tail_ESS
## sd(Intercept)                          5812     5571
## sd(self_contribution_c)                4054     6726
## cor(Intercept,self_contribution_c)     6091     7771
## 
## Population-Level Effects: 
##                                      Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1]                            -5.47      0.36    -6.18    -4.78 1.00
## Intercept[2]                            -1.86      0.29    -2.44    -1.29 1.00
## Intercept[3]                             0.86      0.29     0.31     1.43 1.00
## Intercept[4]                             3.13      0.31     2.54     3.76 1.00
## Intercept[5]                             5.76      0.38     5.04     6.54 1.00
## categoryabstract                        -0.03      0.22    -0.46     0.40 1.00
## self_contribution_c                      0.05      0.01     0.03     0.07 1.00
## difficulty_c                            -0.03      0.00    -0.04    -0.02 1.00
## categoryabstract:self_contribution_c     0.00      0.01    -0.02     0.03 1.00
##                                      Bulk_ESS Tail_ESS
## Intercept[1]                             3763     6919
## Intercept[2]                             3101     5445
## Intercept[3]                             3125     5443
## Intercept[4]                             3376     5949
## Intercept[5]                             4277     7263
## categoryabstract                         6368     8190
## self_contribution_c                      5850     7587
## difficulty_c                            12522     9687
## categoryabstract:self_contribution_c     7247     8878
## 
## Family Specific Parameters: 
##      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc     1.00      0.00     1.00     1.00   NA       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(IOS_self_mdl,
           'categoryabstract < 0')
## Hypothesis Tests for class b:
##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) < 0    -0.03      0.22    -0.38     0.33        1.2
##   Post.Prob Star
## 1      0.55     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_self_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.03         0    -0.04    -0.03        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_self_mdl,
           'self_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0     0.05      0.01     0.03     0.07        Inf
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_self_mdl,
           'categoryabstract:self_contribution_c  > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract... > 0        0      0.01    -0.02     0.02       1.57
##   Post.Prob Star
## 1      0.61     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Re-do the other main model, the one with closeness_01 as dependent variable, this time also with a difficulty_c control covariate:

dist_self_mdl <- brm(bf(closeness_01 ~ 
                       
                       # Fixed effects:
                       
                       1 +
                       category +
                       self_contribution_c +
                       difficulty_c +
                       category:self_contribution_c +
                                      
                       # Random effects:
                                      
                       (1 +
                          category +
                          self_contribution_c +
                          category:self_contribution_c|participant) +
                       (1 + self_contribution_c|word),
                       phi ~ 1 + category),
           
                     data = df,
                     family = Beta,
           
                     # MCMC settings:
           
                     seed = 42,
                     init = 0,
                     cores = 4,
                     iter = 6000,
                     warmup = 3000,
                     save_pars = save_pars(all = TRUE), # for bayes factors
                     control = list(adapt_delta = 0.99))

# Save model:

save(dist_self_mdl,
     file = '../models_E2/dist_self_mdl.Rdata')

The corresponding null model:

dist_self_null <- brm(bf(closeness_01 ~ 
                       
                       # Fixed effects:
                       
                       1 +
                       category +
                       self_contribution_c +
                       difficulty_c +
                                      
                       # Random effects:
                                      
                       (1 +
                          category +
                          self_contribution_c +
                          category:self_contribution_c|participant) +
                       (1 + self_contribution_c|word),
                       phi ~ 1 + category),
           
                     data = df,
                     family = Beta,
           
                     # MCMC settings:
           
                     seed = 42,
                     init = 0,
                     cores = 4,
                     iter = 6000,
                     warmup = 3000,
                     save_pars = save_pars(all = TRUE), # for bayes factors
                     control = list(adapt_delta = 0.99))

# Save model:

save(dist_self_null,
     file = '../models_E2/dist_self_null.Rdata')

Load model:

load('../models_E2/dist_self_mdl.Rdata')
load('../models_E2/dist_self_null.Rdata')

Show priors:

prior_summary(dist_self_mdl)
##                 prior     class                                 coef
##                (flat)         b                                     
##                (flat)         b                     categoryabstract
##                (flat)         b categoryabstract:self_contribution_c
##                (flat)         b                         difficulty_c
##                (flat)         b                  self_contribution_c
##                (flat)         b                                     
##                (flat)         b                     categoryabstract
##  student_t(3, 0, 2.5) Intercept                                     
##  student_t(3, 0, 2.5) Intercept                                     
##  lkj_corr_cholesky(1)         L                                     
##  lkj_corr_cholesky(1)         L                                     
##  lkj_corr_cholesky(1)         L                                     
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                     categoryabstract
##  student_t(3, 0, 2.5)        sd categoryabstract:self_contribution_c
##  student_t(3, 0, 2.5)        sd                            Intercept
##  student_t(3, 0, 2.5)        sd                  self_contribution_c
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                            Intercept
##  student_t(3, 0, 2.5)        sd                  self_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                    phi                  default
##                    phi             (vectorized)
##                                         default
##                    phi                  default
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
prior_summary(dist_self_null)
##                 prior     class                                 coef
##                (flat)         b                                     
##                (flat)         b                     categoryabstract
##                (flat)         b                         difficulty_c
##                (flat)         b                  self_contribution_c
##                (flat)         b                                     
##                (flat)         b                     categoryabstract
##  student_t(3, 0, 2.5) Intercept                                     
##  student_t(3, 0, 2.5) Intercept                                     
##  lkj_corr_cholesky(1)         L                                     
##  lkj_corr_cholesky(1)         L                                     
##  lkj_corr_cholesky(1)         L                                     
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                     categoryabstract
##  student_t(3, 0, 2.5)        sd categoryabstract:self_contribution_c
##  student_t(3, 0, 2.5)        sd                            Intercept
##  student_t(3, 0, 2.5)        sd                  self_contribution_c
##  student_t(3, 0, 2.5)        sd                                     
##  student_t(3, 0, 2.5)        sd                            Intercept
##  student_t(3, 0, 2.5)        sd                  self_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                    phi                  default
##                    phi             (vectorized)
##                                         default
##                    phi                  default
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)

Bayes factors for both:

# Compute:

dist_self_bf <- bayes_factor(dist_self_mdl, dist_self_null)

# Save:

save(dist_self_bf,
     file = '../models_E2/dist_self_bf.RData')

Show Bayes factor:

# Load:

load('../models_E2/dist_self_bf.RData')

# Show:

dist_self_bf
## Estimated Bayes factor in favor of dist_self_mdl over dist_self_null: 0.03459

Check posterior predictive checks of the mixed beta regression:

pp_check(dist_self_mdl, ndraws = 100)

Check this model:

dist_self_mdl
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: closeness_01 ~ 1 + category + self_contribution_c + difficulty_c + category:self_contribution_c + (1 + category + self_contribution_c + category:self_contribution_c | participant) + (1 + self_contribution_c | word) 
##          phi ~ 1 + category
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                               Estimate
## sd(Intercept)                                                     0.86
## sd(categoryabstract)                                              0.49
## sd(self_contribution_c)                                           0.02
## sd(categoryabstract:self_contribution_c)                          0.01
## cor(Intercept,categoryabstract)                                  -0.33
## cor(Intercept,self_contribution_c)                                0.02
## cor(categoryabstract,self_contribution_c)                        -0.11
## cor(Intercept,categoryabstract:self_contribution_c)               0.01
## cor(categoryabstract,categoryabstract:self_contribution_c)        0.18
## cor(self_contribution_c,categoryabstract:self_contribution_c)    -0.45
##                                                               Est.Error
## sd(Intercept)                                                      0.07
## sd(categoryabstract)                                               0.07
## sd(self_contribution_c)                                            0.00
## sd(categoryabstract:self_contribution_c)                           0.01
## cor(Intercept,categoryabstract)                                    0.12
## cor(Intercept,self_contribution_c)                                 0.13
## cor(categoryabstract,self_contribution_c)                          0.15
## cor(Intercept,categoryabstract:self_contribution_c)                0.24
## cor(categoryabstract,categoryabstract:self_contribution_c)         0.25
## cor(self_contribution_c,categoryabstract:self_contribution_c)      0.30
##                                                               l-95% CI u-95% CI
## sd(Intercept)                                                     0.74     1.00
## sd(categoryabstract)                                              0.35     0.62
## sd(self_contribution_c)                                           0.02     0.03
## sd(categoryabstract:self_contribution_c)                          0.00     0.02
## cor(Intercept,categoryabstract)                                  -0.54    -0.08
## cor(Intercept,self_contribution_c)                               -0.23     0.28
## cor(categoryabstract,self_contribution_c)                        -0.40     0.18
## cor(Intercept,categoryabstract:self_contribution_c)              -0.52     0.49
## cor(categoryabstract,categoryabstract:self_contribution_c)       -0.29     0.70
## cor(self_contribution_c,categoryabstract:self_contribution_c)    -0.86     0.36
##                                                               Rhat Bulk_ESS
## sd(Intercept)                                                 1.00     2783
## sd(categoryabstract)                                          1.00      991
## sd(self_contribution_c)                                       1.01     1072
## sd(categoryabstract:self_contribution_c)                      1.01      465
## cor(Intercept,categoryabstract)                               1.00     3371
## cor(Intercept,self_contribution_c)                            1.00     4074
## cor(categoryabstract,self_contribution_c)                     1.00     2718
## cor(Intercept,categoryabstract:self_contribution_c)           1.00     5985
## cor(categoryabstract,categoryabstract:self_contribution_c)    1.00     3369
## cor(self_contribution_c,categoryabstract:self_contribution_c) 1.00     1723
##                                                               Tail_ESS
## sd(Intercept)                                                     5067
## sd(categoryabstract)                                              2754
## sd(self_contribution_c)                                           3057
## sd(categoryabstract:self_contribution_c)                          1198
## cor(Intercept,categoryabstract)                                   6112
## cor(Intercept,self_contribution_c)                                6854
## cor(categoryabstract,self_contribution_c)                         4643
## cor(Intercept,categoryabstract:self_contribution_c)               3139
## cor(categoryabstract,categoryabstract:self_contribution_c)        2874
## cor(self_contribution_c,categoryabstract:self_contribution_c)     1847
## 
## ~word (Number of levels: 32) 
##                                    Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                          0.07      0.03     0.02     0.12 1.00
## sd(self_contribution_c)                0.00      0.00     0.00     0.01 1.00
## cor(Intercept,self_contribution_c)     0.52      0.39    -0.50     0.98 1.00
##                                    Bulk_ESS Tail_ESS
## sd(Intercept)                          3554     2841
## sd(self_contribution_c)                3328     3876
## cor(Intercept,self_contribution_c)     4568     5221
## 
## Population-Level Effects: 
##                                      Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept                                0.93      0.08     0.76     1.09 1.00
## phi_Intercept                            3.41      0.08     3.26     3.57 1.00
## categoryabstract                        -0.00      0.06    -0.13     0.12 1.00
## self_contribution_c                      0.01      0.00     0.01     0.02 1.00
## difficulty_c                            -0.01      0.00    -0.01    -0.01 1.00
## categoryabstract:self_contribution_c     0.00      0.00    -0.01     0.01 1.00
## phi_categoryabstract                    -0.39      0.12    -0.62    -0.17 1.00
##                                      Bulk_ESS Tail_ESS
## Intercept                                1794     3425
## phi_Intercept                            5543     8344
## categoryabstract                         5843     7564
## self_contribution_c                      5259     7560
## difficulty_c                            13806    11659
## categoryabstract:self_contribution_c     7311     7923
## phi_categoryabstract                     8706     9480
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(dist_self_mdl,
           'categoryabstract > 0')
## Hypothesis Tests for class b:
##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) > 0        0      0.06    -0.11      0.1       0.89
##   Post.Prob Star
## 1      0.47     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_self_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.01         0    -0.01    -0.01        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_self_mdl,
           'self_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0     0.01         0     0.01     0.02       5999
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_self_mdl,
           'categoryabstract:self_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract... > 0        0         0        0     0.01       1.39
##   Post.Prob Star
## 1      0.58     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

13 Subcluster models: other-contribution

Do the main analysis of IOS with difficulty as a covariate predictor, to control for this.

subcluster_mdl <- brm(IOS ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        other_contribution_c +
                        difficulty_c +
                        subcluster:other_contribution_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           other_contribution_c +
                           subcluster:other_contribution_c|participant) +
                        (1 + other_contribution_c|word),
           
                      data = df,
                      family = cumulative,
           
                      # MCMC settings:
                               
                      seed = 42,
                      cores = 4,
                      iter = 6000,
                      warmup = 3000,
                      control = list(adapt_delta = 0.99))

# Save model:

save(subcluster_mdl,
     file = '../models_E2/subcluster_mdl.Rdata')

The corresponding null model:

subcluster_null <- brm(IOS ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        other_contribution_c +
                        difficulty_c +
                        subcluster:other_contribution_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           other_contribution_c +
                           subcluster:other_contribution_c|participant) +
                        (1 + other_contribution_c|word),
           
                      data = df,
                      family = cumulative,
           
                      # MCMC settings:
                               
                      seed = 42,
                      cores = 4,
                      iter = 6000,
                      warmup = 3000,
                      control = list(adapt_delta = 0.99))

# Save model:

save(subcluster_null,
     file = '../models_E2/subcluster_null.Rdata')

Load model:

load('../models_E2/subcluster_mdl.Rdata')

Show priors:

prior_summary(subcluster_mdl)
##                 prior     class                                   coef
##                (flat)         b                                       
##                (flat)         b                           difficulty_c
##                (flat)         b                   other_contribution_c
##                (flat)         b                      subclusterConc_an
##                (flat)         b subclusterConc_an:other_contribution_c
##                (flat)         b                      subclusterConc_in
##                (flat)         b subclusterConc_in:other_contribution_c
##                (flat)         b                           subclusterEM
##                (flat)         b      subclusterEM:other_contribution_c
##                (flat)         b                           subclusterPS
##                (flat)         b      subclusterPS:other_contribution_c
##                (flat)         b                           subclusterSS
##                (flat)         b      subclusterSS:other_contribution_c
##  student_t(3, 0, 2.5) Intercept                                       
##  student_t(3, 0, 2.5) Intercept                                      1
##  student_t(3, 0, 2.5) Intercept                                      2
##  student_t(3, 0, 2.5) Intercept                                      3
##  student_t(3, 0, 2.5) Intercept                                      4
##  student_t(3, 0, 2.5) Intercept                                      5
##  lkj_corr_cholesky(1)         L                                       
##  lkj_corr_cholesky(1)         L                                       
##  lkj_corr_cholesky(1)         L                                       
##  student_t(3, 0, 2.5)        sd                                       
##  student_t(3, 0, 2.5)        sd                                       
##  student_t(3, 0, 2.5)        sd                              Intercept
##  student_t(3, 0, 2.5)        sd                   other_contribution_c
##  student_t(3, 0, 2.5)        sd                      subclusterConc_an
##  student_t(3, 0, 2.5)        sd subclusterConc_an:other_contribution_c
##  student_t(3, 0, 2.5)        sd                      subclusterConc_in
##  student_t(3, 0, 2.5)        sd subclusterConc_in:other_contribution_c
##  student_t(3, 0, 2.5)        sd                           subclusterEM
##  student_t(3, 0, 2.5)        sd      subclusterEM:other_contribution_c
##  student_t(3, 0, 2.5)        sd                           subclusterPS
##  student_t(3, 0, 2.5)        sd      subclusterPS:other_contribution_c
##  student_t(3, 0, 2.5)        sd                           subclusterSS
##  student_t(3, 0, 2.5)        sd      subclusterSS:other_contribution_c
##  student_t(3, 0, 2.5)        sd                                       
##  student_t(3, 0, 2.5)        sd                              Intercept
##  student_t(3, 0, 2.5)        sd                   other_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)

Check posterior predictive checks of the mixed beta regression:

pp_check(subcluster_mdl, ndraws = 100)

Check this model:

subcluster_mdl
##  Family: cumulative 
##   Links: mu = logit; disc = identity 
## Formula: IOS ~ 1 + subcluster + other_contribution_c + difficulty_c + subcluster:other_contribution_c + (1 + subcluster + other_contribution_c + subcluster:other_contribution_c | participant) + (1 + other_contribution_c | word) 
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                                    Estimate
## sd(Intercept)                                                                          2.92
## sd(subclusterConc_an)                                                                  1.41
## sd(subclusterConc_in)                                                                  1.61
## sd(subclusterEM)                                                                       0.50
## sd(subclusterPS)                                                                       0.70
## sd(subclusterSS)                                                                       0.60
## sd(other_contribution_c)                                                               0.05
## sd(subclusterConc_an:other_contribution_c)                                             0.05
## sd(subclusterConc_in:other_contribution_c)                                             0.05
## sd(subclusterEM:other_contribution_c)                                                  0.06
## sd(subclusterPS:other_contribution_c)                                                  0.05
## sd(subclusterSS:other_contribution_c)                                                  0.05
## cor(Intercept,subclusterConc_an)                                                      -0.09
## cor(Intercept,subclusterConc_in)                                                      -0.11
## cor(subclusterConc_an,subclusterConc_in)                                               0.66
## cor(Intercept,subclusterEM)                                                           -0.04
## cor(subclusterConc_an,subclusterEM)                                                   -0.07
## cor(subclusterConc_in,subclusterEM)                                                   -0.11
## cor(Intercept,subclusterPS)                                                           -0.02
## cor(subclusterConc_an,subclusterPS)                                                   -0.21
## cor(subclusterConc_in,subclusterPS)                                                   -0.18
## cor(subclusterEM,subclusterPS)                                                         0.09
## cor(Intercept,subclusterSS)                                                           -0.02
## cor(subclusterConc_an,subclusterSS)                                                    0.03
## cor(subclusterConc_in,subclusterSS)                                                    0.05
## cor(subclusterEM,subclusterSS)                                                         0.02
## cor(subclusterPS,subclusterSS)                                                        -0.00
## cor(Intercept,other_contribution_c)                                                    0.04
## cor(subclusterConc_an,other_contribution_c)                                            0.01
## cor(subclusterConc_in,other_contribution_c)                                           -0.06
## cor(subclusterEM,other_contribution_c)                                                -0.08
## cor(subclusterPS,other_contribution_c)                                                 0.01
## cor(subclusterSS,other_contribution_c)                                                 0.07
## cor(Intercept,subclusterConc_an:other_contribution_c)                                  0.20
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                         -0.04
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                         -0.05
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                               0.00
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                              -0.03
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                               0.03
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                       0.05
## cor(Intercept,subclusterConc_in:other_contribution_c)                                  0.01
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                         -0.01
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                          0.07
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                              -0.06
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                               0.10
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                              -0.07
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                       0.00
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)     0.32
## cor(Intercept,subclusterEM:other_contribution_c)                                      -0.04
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                               0.04
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                              -0.13
## cor(subclusterEM,subclusterEM:other_contribution_c)                                    0.03
## cor(subclusterPS,subclusterEM:other_contribution_c)                                   -0.10
## cor(subclusterSS,subclusterEM:other_contribution_c)                                    0.05
## cor(other_contribution_c,subclusterEM:other_contribution_c)                           -0.12
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)          0.02
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)         -0.25
## cor(Intercept,subclusterPS:other_contribution_c)                                       0.15
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                               0.05
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                               0.12
## cor(subclusterEM,subclusterPS:other_contribution_c)                                   -0.06
## cor(subclusterPS,subclusterPS:other_contribution_c)                                   -0.06
## cor(subclusterSS,subclusterPS:other_contribution_c)                                    0.04
## cor(other_contribution_c,subclusterPS:other_contribution_c)                            0.00
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)         -0.06
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)         -0.11
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)               0.08
## cor(Intercept,subclusterSS:other_contribution_c)                                       0.02
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                              -0.06
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                              -0.12
## cor(subclusterEM,subclusterSS:other_contribution_c)                                    0.04
## cor(subclusterPS,subclusterSS:other_contribution_c)                                    0.04
## cor(subclusterSS,subclusterSS:other_contribution_c)                                   -0.05
## cor(other_contribution_c,subclusterSS:other_contribution_c)                           -0.07
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)         -0.14
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)         -0.12
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)               0.15
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)               0.14
##                                                                                    Est.Error
## sd(Intercept)                                                                           0.27
## sd(subclusterConc_an)                                                                   0.43
## sd(subclusterConc_in)                                                                   0.42
## sd(subclusterEM)                                                                        0.37
## sd(subclusterPS)                                                                        0.44
## sd(subclusterSS)                                                                        0.43
## sd(other_contribution_c)                                                                0.01
## sd(subclusterConc_an:other_contribution_c)                                              0.03
## sd(subclusterConc_in:other_contribution_c)                                              0.02
## sd(subclusterEM:other_contribution_c)                                                   0.02
## sd(subclusterPS:other_contribution_c)                                                   0.03
## sd(subclusterSS:other_contribution_c)                                                   0.03
## cor(Intercept,subclusterConc_an)                                                        0.16
## cor(Intercept,subclusterConc_in)                                                        0.16
## cor(subclusterConc_an,subclusterConc_in)                                                0.19
## cor(Intercept,subclusterEM)                                                             0.25
## cor(subclusterConc_an,subclusterEM)                                                     0.27
## cor(subclusterConc_in,subclusterEM)                                                     0.27
## cor(Intercept,subclusterPS)                                                             0.24
## cor(subclusterConc_an,subclusterPS)                                                     0.27
## cor(subclusterConc_in,subclusterPS)                                                     0.26
## cor(subclusterEM,subclusterPS)                                                          0.28
## cor(Intercept,subclusterSS)                                                             0.25
## cor(subclusterConc_an,subclusterSS)                                                     0.27
## cor(subclusterConc_in,subclusterSS)                                                     0.27
## cor(subclusterEM,subclusterSS)                                                          0.28
## cor(subclusterPS,subclusterSS)                                                          0.27
## cor(Intercept,other_contribution_c)                                                     0.17
## cor(subclusterConc_an,other_contribution_c)                                             0.22
## cor(subclusterConc_in,other_contribution_c)                                             0.21
## cor(subclusterEM,other_contribution_c)                                                  0.27
## cor(subclusterPS,other_contribution_c)                                                  0.26
## cor(subclusterSS,other_contribution_c)                                                  0.27
## cor(Intercept,subclusterConc_an:other_contribution_c)                                   0.22
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                           0.24
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                           0.24
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                                0.27
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                                0.27
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                                0.27
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                        0.25
## cor(Intercept,subclusterConc_in:other_contribution_c)                                   0.21
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                           0.25
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                           0.23
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                                0.28
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                                0.27
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                                0.28
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                        0.25
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)      0.30
## cor(Intercept,subclusterEM:other_contribution_c)                                        0.19
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                                0.23
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                                0.23
## cor(subclusterEM,subclusterEM:other_contribution_c)                                     0.27
## cor(subclusterPS,subclusterEM:other_contribution_c)                                     0.27
## cor(subclusterSS,subclusterEM:other_contribution_c)                                     0.27
## cor(other_contribution_c,subclusterEM:other_contribution_c)                             0.24
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)           0.25
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)           0.25
## cor(Intercept,subclusterPS:other_contribution_c)                                        0.22
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                                0.25
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                                0.25
## cor(subclusterEM,subclusterPS:other_contribution_c)                                     0.28
## cor(subclusterPS,subclusterPS:other_contribution_c)                                     0.27
## cor(subclusterSS,subclusterPS:other_contribution_c)                                     0.27
## cor(other_contribution_c,subclusterPS:other_contribution_c)                             0.25
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)           0.26
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)           0.26
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)                0.26
## cor(Intercept,subclusterSS:other_contribution_c)                                        0.23
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                                0.26
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                                0.26
## cor(subclusterEM,subclusterSS:other_contribution_c)                                     0.27
## cor(subclusterPS,subclusterSS:other_contribution_c)                                     0.27
## cor(subclusterSS,subclusterSS:other_contribution_c)                                     0.27
## cor(other_contribution_c,subclusterSS:other_contribution_c)                             0.27
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)           0.27
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)           0.27
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)                0.27
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)                0.28
##                                                                                    l-95% CI
## sd(Intercept)                                                                          2.44
## sd(subclusterConc_an)                                                                  0.35
## sd(subclusterConc_in)                                                                  0.60
## sd(subclusterEM)                                                                       0.02
## sd(subclusterPS)                                                                       0.04
## sd(subclusterSS)                                                                       0.02
## sd(other_contribution_c)                                                               0.02
## sd(subclusterConc_an:other_contribution_c)                                             0.00
## sd(subclusterConc_in:other_contribution_c)                                             0.01
## sd(subclusterEM:other_contribution_c)                                                  0.02
## sd(subclusterPS:other_contribution_c)                                                  0.00
## sd(subclusterSS:other_contribution_c)                                                  0.00
## cor(Intercept,subclusterConc_an)                                                      -0.39
## cor(Intercept,subclusterConc_in)                                                      -0.40
## cor(subclusterConc_an,subclusterConc_in)                                               0.11
## cor(Intercept,subclusterEM)                                                           -0.51
## cor(subclusterConc_an,subclusterEM)                                                   -0.56
## cor(subclusterConc_in,subclusterEM)                                                   -0.60
## cor(Intercept,subclusterPS)                                                           -0.48
## cor(subclusterConc_an,subclusterPS)                                                   -0.68
## cor(subclusterConc_in,subclusterPS)                                                   -0.64
## cor(subclusterEM,subclusterPS)                                                        -0.47
## cor(Intercept,subclusterSS)                                                           -0.51
## cor(subclusterConc_an,subclusterSS)                                                   -0.49
## cor(subclusterConc_in,subclusterSS)                                                   -0.48
## cor(subclusterEM,subclusterSS)                                                        -0.51
## cor(subclusterPS,subclusterSS)                                                        -0.52
## cor(Intercept,other_contribution_c)                                                   -0.30
## cor(subclusterConc_an,other_contribution_c)                                           -0.43
## cor(subclusterConc_in,other_contribution_c)                                           -0.46
## cor(subclusterEM,other_contribution_c)                                                -0.57
## cor(subclusterPS,other_contribution_c)                                                -0.48
## cor(subclusterSS,other_contribution_c)                                                -0.47
## cor(Intercept,subclusterConc_an:other_contribution_c)                                 -0.28
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                         -0.49
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                         -0.51
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                              -0.51
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                              -0.54
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                              -0.51
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                      -0.43
## cor(Intercept,subclusterConc_in:other_contribution_c)                                 -0.41
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                         -0.48
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                         -0.39
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                              -0.58
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                              -0.44
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                              -0.58
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                      -0.46
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)    -0.33
## cor(Intercept,subclusterEM:other_contribution_c)                                      -0.42
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                              -0.43
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                              -0.56
## cor(subclusterEM,subclusterEM:other_contribution_c)                                   -0.50
## cor(subclusterPS,subclusterEM:other_contribution_c)                                   -0.59
## cor(subclusterSS,subclusterEM:other_contribution_c)                                   -0.48
## cor(other_contribution_c,subclusterEM:other_contribution_c)                           -0.56
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)         -0.47
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)         -0.68
## cor(Intercept,subclusterPS:other_contribution_c)                                      -0.29
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                              -0.44
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                              -0.38
## cor(subclusterEM,subclusterPS:other_contribution_c)                                   -0.58
## cor(subclusterPS,subclusterPS:other_contribution_c)                                   -0.56
## cor(subclusterSS,subclusterPS:other_contribution_c)                                   -0.49
## cor(other_contribution_c,subclusterPS:other_contribution_c)                           -0.48
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)         -0.54
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)         -0.58
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)              -0.44
## cor(Intercept,subclusterSS:other_contribution_c)                                      -0.45
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                              -0.55
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                              -0.59
## cor(subclusterEM,subclusterSS:other_contribution_c)                                   -0.49
## cor(subclusterPS,subclusterSS:other_contribution_c)                                   -0.49
## cor(subclusterSS,subclusterSS:other_contribution_c)                                   -0.57
## cor(other_contribution_c,subclusterSS:other_contribution_c)                           -0.58
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)         -0.62
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)         -0.61
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)              -0.40
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)              -0.44
##                                                                                    u-95% CI
## sd(Intercept)                                                                          3.50
## sd(subclusterConc_an)                                                                  2.14
## sd(subclusterConc_in)                                                                  2.34
## sd(subclusterEM)                                                                       1.35
## sd(subclusterPS)                                                                       1.62
## sd(subclusterSS)                                                                       1.56
## sd(other_contribution_c)                                                               0.08
## sd(subclusterConc_an:other_contribution_c)                                             0.10
## sd(subclusterConc_in:other_contribution_c)                                             0.10
## sd(subclusterEM:other_contribution_c)                                                  0.10
## sd(subclusterPS:other_contribution_c)                                                  0.10
## sd(subclusterSS:other_contribution_c)                                                  0.10
## cor(Intercept,subclusterConc_an)                                                       0.25
## cor(Intercept,subclusterConc_in)                                                       0.22
## cor(subclusterConc_an,subclusterConc_in)                                               0.89
## cor(Intercept,subclusterEM)                                                            0.47
## cor(subclusterConc_an,subclusterEM)                                                    0.46
## cor(subclusterConc_in,subclusterEM)                                                    0.44
## cor(Intercept,subclusterPS)                                                            0.47
## cor(subclusterConc_an,subclusterPS)                                                    0.37
## cor(subclusterConc_in,subclusterPS)                                                    0.38
## cor(subclusterEM,subclusterPS)                                                         0.60
## cor(Intercept,subclusterSS)                                                            0.48
## cor(subclusterConc_an,subclusterSS)                                                    0.54
## cor(subclusterConc_in,subclusterSS)                                                    0.56
## cor(subclusterEM,subclusterSS)                                                         0.54
## cor(subclusterPS,subclusterSS)                                                         0.53
## cor(Intercept,other_contribution_c)                                                    0.37
## cor(subclusterConc_an,other_contribution_c)                                            0.42
## cor(subclusterConc_in,other_contribution_c)                                            0.34
## cor(subclusterEM,other_contribution_c)                                                 0.46
## cor(subclusterPS,other_contribution_c)                                                 0.53
## cor(subclusterSS,other_contribution_c)                                                 0.58
## cor(Intercept,subclusterConc_an:other_contribution_c)                                  0.58
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                          0.43
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                          0.43
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                               0.52
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                               0.49
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                               0.55
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                       0.53
## cor(Intercept,subclusterConc_in:other_contribution_c)                                  0.41
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                          0.47
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                          0.51
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                               0.48
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                               0.59
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                               0.48
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                       0.51
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)     0.78
## cor(Intercept,subclusterEM:other_contribution_c)                                       0.35
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                               0.48
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                               0.32
## cor(subclusterEM,subclusterEM:other_contribution_c)                                    0.54
## cor(subclusterPS,subclusterEM:other_contribution_c)                                    0.45
## cor(subclusterSS,subclusterEM:other_contribution_c)                                    0.56
## cor(other_contribution_c,subclusterEM:other_contribution_c)                            0.39
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)          0.50
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)          0.30
## cor(Intercept,subclusterPS:other_contribution_c)                                       0.56
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                               0.53
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                               0.58
## cor(subclusterEM,subclusterPS:other_contribution_c)                                    0.48
## cor(subclusterPS,subclusterPS:other_contribution_c)                                    0.46
## cor(subclusterSS,subclusterPS:other_contribution_c)                                    0.56
## cor(other_contribution_c,subclusterPS:other_contribution_c)                            0.50
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)          0.44
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)          0.42
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)               0.56
## cor(Intercept,subclusterSS:other_contribution_c)                                       0.46
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                               0.45
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                               0.40
## cor(subclusterEM,subclusterSS:other_contribution_c)                                    0.57
## cor(subclusterPS,subclusterSS:other_contribution_c)                                    0.56
## cor(subclusterSS,subclusterSS:other_contribution_c)                                    0.48
## cor(other_contribution_c,subclusterSS:other_contribution_c)                            0.47
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)          0.42
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)          0.43
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)               0.62
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)               0.64
##                                                                                    Rhat
## sd(Intercept)                                                                      1.00
## sd(subclusterConc_an)                                                              1.00
## sd(subclusterConc_in)                                                              1.00
## sd(subclusterEM)                                                                   1.00
## sd(subclusterPS)                                                                   1.00
## sd(subclusterSS)                                                                   1.00
## sd(other_contribution_c)                                                           1.00
## sd(subclusterConc_an:other_contribution_c)                                         1.01
## sd(subclusterConc_in:other_contribution_c)                                         1.00
## sd(subclusterEM:other_contribution_c)                                              1.00
## sd(subclusterPS:other_contribution_c)                                              1.00
## sd(subclusterSS:other_contribution_c)                                              1.00
## cor(Intercept,subclusterConc_an)                                                   1.00
## cor(Intercept,subclusterConc_in)                                                   1.00
## cor(subclusterConc_an,subclusterConc_in)                                           1.00
## cor(Intercept,subclusterEM)                                                        1.00
## cor(subclusterConc_an,subclusterEM)                                                1.00
## cor(subclusterConc_in,subclusterEM)                                                1.00
## cor(Intercept,subclusterPS)                                                        1.00
## cor(subclusterConc_an,subclusterPS)                                                1.00
## cor(subclusterConc_in,subclusterPS)                                                1.00
## cor(subclusterEM,subclusterPS)                                                     1.00
## cor(Intercept,subclusterSS)                                                        1.00
## cor(subclusterConc_an,subclusterSS)                                                1.00
## cor(subclusterConc_in,subclusterSS)                                                1.00
## cor(subclusterEM,subclusterSS)                                                     1.00
## cor(subclusterPS,subclusterSS)                                                     1.00
## cor(Intercept,other_contribution_c)                                                1.00
## cor(subclusterConc_an,other_contribution_c)                                        1.00
## cor(subclusterConc_in,other_contribution_c)                                        1.00
## cor(subclusterEM,other_contribution_c)                                             1.00
## cor(subclusterPS,other_contribution_c)                                             1.00
## cor(subclusterSS,other_contribution_c)                                             1.00
## cor(Intercept,subclusterConc_an:other_contribution_c)                              1.00
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                      1.00
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                      1.00
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                           1.00
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                           1.00
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                           1.00
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                   1.00
## cor(Intercept,subclusterConc_in:other_contribution_c)                              1.00
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                      1.00
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                      1.00
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                           1.00
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                           1.00
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                           1.00
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                   1.00
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 1.00
## cor(Intercept,subclusterEM:other_contribution_c)                                   1.00
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                           1.00
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                           1.00
## cor(subclusterEM,subclusterEM:other_contribution_c)                                1.00
## cor(subclusterPS,subclusterEM:other_contribution_c)                                1.00
## cor(subclusterSS,subclusterEM:other_contribution_c)                                1.00
## cor(other_contribution_c,subclusterEM:other_contribution_c)                        1.00
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)      1.00
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)      1.00
## cor(Intercept,subclusterPS:other_contribution_c)                                   1.00
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                           1.00
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                           1.00
## cor(subclusterEM,subclusterPS:other_contribution_c)                                1.00
## cor(subclusterPS,subclusterPS:other_contribution_c)                                1.00
## cor(subclusterSS,subclusterPS:other_contribution_c)                                1.00
## cor(other_contribution_c,subclusterPS:other_contribution_c)                        1.00
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)      1.00
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)      1.00
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)           1.00
## cor(Intercept,subclusterSS:other_contribution_c)                                   1.00
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                           1.00
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                           1.00
## cor(subclusterEM,subclusterSS:other_contribution_c)                                1.00
## cor(subclusterPS,subclusterSS:other_contribution_c)                                1.00
## cor(subclusterSS,subclusterSS:other_contribution_c)                                1.00
## cor(other_contribution_c,subclusterSS:other_contribution_c)                        1.00
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)      1.00
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)      1.00
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)           1.00
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)           1.00
##                                                                                    Bulk_ESS
## sd(Intercept)                                                                          3287
## sd(subclusterConc_an)                                                                   727
## sd(subclusterConc_in)                                                                   967
## sd(subclusterEM)                                                                       1692
## sd(subclusterPS)                                                                       1956
## sd(subclusterSS)                                                                       2401
## sd(other_contribution_c)                                                               1985
## sd(subclusterConc_an:other_contribution_c)                                              761
## sd(subclusterConc_in:other_contribution_c)                                              745
## sd(subclusterEM:other_contribution_c)                                                  2302
## sd(subclusterPS:other_contribution_c)                                                  1829
## sd(subclusterSS:other_contribution_c)                                                  2098
## cor(Intercept,subclusterConc_an)                                                       7264
## cor(Intercept,subclusterConc_in)                                                       7404
## cor(subclusterConc_an,subclusterConc_in)                                               1110
## cor(Intercept,subclusterEM)                                                           17472
## cor(subclusterConc_an,subclusterEM)                                                    9347
## cor(subclusterConc_in,subclusterEM)                                                    8370
## cor(Intercept,subclusterPS)                                                           13544
## cor(subclusterConc_an,subclusterPS)                                                    5026
## cor(subclusterConc_in,subclusterPS)                                                    7553
## cor(subclusterEM,subclusterPS)                                                         6523
## cor(Intercept,subclusterSS)                                                           18693
## cor(subclusterConc_an,subclusterSS)                                                   10395
## cor(subclusterConc_in,subclusterSS)                                                   10305
## cor(subclusterEM,subclusterSS)                                                         9133
## cor(subclusterPS,subclusterSS)                                                         9961
## cor(Intercept,other_contribution_c)                                                    8664
## cor(subclusterConc_an,other_contribution_c)                                            2849
## cor(subclusterConc_in,other_contribution_c)                                            3603
## cor(subclusterEM,other_contribution_c)                                                 2005
## cor(subclusterPS,other_contribution_c)                                                 2466
## cor(subclusterSS,other_contribution_c)                                                 2369
## cor(Intercept,subclusterConc_an:other_contribution_c)                                  7834
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                          6297
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                          6988
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                               4485
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                               4027
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                               5120
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                       6447
## cor(Intercept,subclusterConc_in:other_contribution_c)                                  7864
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                          3973
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                          6143
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                               3232
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                               3388
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                               4435
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                       5645
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)     1073
## cor(Intercept,subclusterEM:other_contribution_c)                                       9676
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                               4970
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                               5590
## cor(subclusterEM,subclusterEM:other_contribution_c)                                    3713
## cor(subclusterPS,subclusterEM:other_contribution_c)                                    3583
## cor(subclusterSS,subclusterEM:other_contribution_c)                                    4956
## cor(other_contribution_c,subclusterEM:other_contribution_c)                            4133
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)          5100
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)          3922
## cor(Intercept,subclusterPS:other_contribution_c)                                      10101
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                               7772
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                               6854
## cor(subclusterEM,subclusterPS:other_contribution_c)                                    5488
## cor(subclusterPS,subclusterPS:other_contribution_c)                                    5515
## cor(subclusterSS,subclusterPS:other_contribution_c)                                    6328
## cor(other_contribution_c,subclusterPS:other_contribution_c)                            6901
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)          6573
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)          5640
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)               6623
## cor(Intercept,subclusterSS:other_contribution_c)                                      15392
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                               8784
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                               8346
## cor(subclusterEM,subclusterSS:other_contribution_c)                                    6621
## cor(subclusterPS,subclusterSS:other_contribution_c)                                    6934
## cor(subclusterSS,subclusterSS:other_contribution_c)                                    7400
## cor(other_contribution_c,subclusterSS:other_contribution_c)                            8725
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)          5415
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)          6761
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)               6706
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)               5164
##                                                                                    Tail_ESS
## sd(Intercept)                                                                          6113
## sd(subclusterConc_an)                                                                   649
## sd(subclusterConc_in)                                                                   919
## sd(subclusterEM)                                                                       3110
## sd(subclusterPS)                                                                       4528
## sd(subclusterSS)                                                                       5071
## sd(other_contribution_c)                                                               1450
## sd(subclusterConc_an:other_contribution_c)                                             2442
## sd(subclusterConc_in:other_contribution_c)                                             2289
## sd(subclusterEM:other_contribution_c)                                                  2509
## sd(subclusterPS:other_contribution_c)                                                  3768
## sd(subclusterSS:other_contribution_c)                                                  4115
## cor(Intercept,subclusterConc_an)                                                       5795
## cor(Intercept,subclusterConc_in)                                                       5939
## cor(subclusterConc_an,subclusterConc_in)                                                858
## cor(Intercept,subclusterEM)                                                            8904
## cor(subclusterConc_an,subclusterEM)                                                    8144
## cor(subclusterConc_in,subclusterEM)                                                    8543
## cor(Intercept,subclusterPS)                                                            8104
## cor(subclusterConc_an,subclusterPS)                                                    6743
## cor(subclusterConc_in,subclusterPS)                                                    8769
## cor(subclusterEM,subclusterPS)                                                         8351
## cor(Intercept,subclusterSS)                                                            9233
## cor(subclusterConc_an,subclusterSS)                                                    9228
## cor(subclusterConc_in,subclusterSS)                                                    9112
## cor(subclusterEM,subclusterSS)                                                         9012
## cor(subclusterPS,subclusterSS)                                                         9421
## cor(Intercept,other_contribution_c)                                                    8263
## cor(subclusterConc_an,other_contribution_c)                                            4891
## cor(subclusterConc_in,other_contribution_c)                                            6654
## cor(subclusterEM,other_contribution_c)                                                 5413
## cor(subclusterPS,other_contribution_c)                                                 4643
## cor(subclusterSS,other_contribution_c)                                                 4316
## cor(Intercept,subclusterConc_an:other_contribution_c)                                  5572
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                          8077
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                          8141
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                               7488
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                               6818
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                               7832
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                       9251
## cor(Intercept,subclusterConc_in:other_contribution_c)                                  7120
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                          7217
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                          7365
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                               6533
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                               6102
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                               6904
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                       8912
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)     4016
## cor(Intercept,subclusterEM:other_contribution_c)                                       8749
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                               6703
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                               6640
## cor(subclusterEM,subclusterEM:other_contribution_c)                                    6988
## cor(subclusterPS,subclusterEM:other_contribution_c)                                    6391
## cor(subclusterSS,subclusterEM:other_contribution_c)                                    7329
## cor(other_contribution_c,subclusterEM:other_contribution_c)                            7653
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)          8476
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)          5517
## cor(Intercept,subclusterPS:other_contribution_c)                                       8781
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                               9027
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                               7782
## cor(subclusterEM,subclusterPS:other_contribution_c)                                    8559
## cor(subclusterPS,subclusterPS:other_contribution_c)                                    8841
## cor(subclusterSS,subclusterPS:other_contribution_c)                                    8974
## cor(other_contribution_c,subclusterPS:other_contribution_c)                            9826
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)          9547
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)          8372
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)               7883
## cor(Intercept,subclusterSS:other_contribution_c)                                       8555
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                               7367
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                               9132
## cor(subclusterEM,subclusterSS:other_contribution_c)                                    8486
## cor(subclusterPS,subclusterSS:other_contribution_c)                                    9553
## cor(subclusterSS,subclusterSS:other_contribution_c)                                    9531
## cor(other_contribution_c,subclusterSS:other_contribution_c)                            9152
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)          9599
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)         10038
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)               8659
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)               9094
## 
## ~word (Number of levels: 32) 
##                                     Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                           0.13      0.09     0.01     0.34 1.00
## sd(other_contribution_c)                0.01      0.01     0.00     0.03 1.00
## cor(Intercept,other_contribution_c)     0.08      0.56    -0.92     0.96 1.00
##                                     Bulk_ESS Tail_ESS
## sd(Intercept)                           5007     6932
## sd(other_contribution_c)                3211     5674
## cor(Intercept,other_contribution_c)     5232     8046
## 
## Population-Level Effects: 
##                                        Estimate Est.Error l-95% CI u-95% CI
## Intercept[1]                              -6.15      0.46    -7.07    -5.27
## Intercept[2]                              -2.06      0.35    -2.76    -1.39
## Intercept[3]                               0.96      0.34     0.29     1.64
## Intercept[4]                               3.47      0.38     2.75     4.24
## Intercept[5]                               6.42      0.47     5.54     7.37
## subclusterConc_an                         -0.08      0.29    -0.65     0.49
## subclusterConc_in                         -0.06      0.31    -0.66     0.54
## subclusterEM                               0.03      0.29    -0.54     0.62
## subclusterPS                              -0.02      0.30    -0.61     0.59
## subclusterSS                              -0.23      0.34    -0.89     0.43
## other_contribution_c                       0.07      0.02     0.04     0.10
## difficulty_c                              -0.03      0.00    -0.04    -0.03
## subclusterConc_an:other_contribution_c    -0.01      0.02    -0.05     0.02
## subclusterConc_in:other_contribution_c     0.00      0.02    -0.03     0.03
## subclusterEM:other_contribution_c         -0.01      0.02    -0.04     0.03
## subclusterPS:other_contribution_c          0.01      0.02    -0.03     0.04
## subclusterSS:other_contribution_c          0.01      0.02    -0.04     0.05
##                                        Rhat Bulk_ESS Tail_ESS
## Intercept[1]                           1.00     3748     6467
## Intercept[2]                           1.00     3940     6742
## Intercept[3]                           1.00     4156     6519
## Intercept[4]                           1.00     4025     6536
## Intercept[5]                           1.00     3885     6845
## subclusterConc_an                      1.00     7950     8891
## subclusterConc_in                      1.00     8299     8522
## subclusterEM                           1.00     9786     9426
## subclusterPS                           1.00    10542     9609
## subclusterSS                           1.00     9487     8554
## other_contribution_c                   1.00     6072     7177
## difficulty_c                           1.00     8617     9326
## subclusterConc_an:other_contribution_c 1.00     6696     7599
## subclusterConc_in:other_contribution_c 1.00     6587     8152
## subclusterEM:other_contribution_c      1.00     7556     7390
## subclusterPS:other_contribution_c      1.00     8699     7894
## subclusterSS:other_contribution_c      1.00     8492     8670
## 
## Family Specific Parameters: 
##      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc     1.00      0.00     1.00     1.00   NA       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(subcluster_mdl,
           'other_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0     0.07      0.02     0.05      0.1      11999
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.03         0    -0.04    -0.03        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_mdl,
           'subclusterConc_an:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_a... < 0    -0.01      0.02    -0.04     0.02       3.54
##   Post.Prob Star
## 1      0.78     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_mdl,
           'subclusterConc_in:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_i... < 0        0      0.02    -0.03     0.03       1.01
##   Post.Prob Star
## 1       0.5     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_mdl,
           'subclusterEM:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:oth... < 0    -0.01      0.02    -0.04     0.02       2.22
##   Post.Prob Star
## 1      0.69     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_mdl,
           'subclusterPS:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:oth... < 0     0.01      0.02    -0.02     0.04       0.52
##   Post.Prob Star
## 1      0.34     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_mdl,
           'subclusterSS:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:oth... < 0     0.01      0.02    -0.03     0.04       0.67
##   Post.Prob Star
## 1       0.4     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Re-do the other main model, the one with closeness_01 as dependent variable, this time also with a difficulty_c control covariate:

subcluster_dist_mdl <- brm(bf(closeness_01 ~ 
                                      
                             # Fixed effects:
                                      
                             1 +
                             subcluster +
                             other_contribution_c +
                             difficulty_c +
                             subcluster:other_contribution_c +
                                      
                             # Random effects:
                                      
                             (1 +
                                subcluster +
                                other_contribution_c +
                                         subcluster:other_contribution_c|participant) +
                             (1 + other_contribution_c|word),
                             phi ~ 1),
           
                           data = df,
                           family = Beta,
           
                           # MCMC settings:
           
                           seed = 42,
                           init = 0,
                           cores = 4,
                           iter = 6000,
                           warmup = 3000,
                           control = list(adapt_delta = 0.99))

# Save model:

save(subcluster_dist_mdl,
     file = '../models_E2/subcluster_dist_mdl.RData')

Load model:

load('../models_E2/subcluster_dist_mdl.Rdata')

Show priors:

prior_summary(subcluster_dist_mdl)
##                 prior     class                                   coef
##                (flat)         b                                       
##                (flat)         b                           difficulty_c
##                (flat)         b                   other_contribution_c
##                (flat)         b                      subclusterConc_an
##                (flat)         b subclusterConc_an:other_contribution_c
##                (flat)         b                      subclusterConc_in
##                (flat)         b subclusterConc_in:other_contribution_c
##                (flat)         b                           subclusterEM
##                (flat)         b      subclusterEM:other_contribution_c
##                (flat)         b                           subclusterPS
##                (flat)         b      subclusterPS:other_contribution_c
##                (flat)         b                           subclusterSS
##                (flat)         b      subclusterSS:other_contribution_c
##  student_t(3, 0, 2.5) Intercept                                       
##  student_t(3, 0, 2.5) Intercept                                       
##  lkj_corr_cholesky(1)         L                                       
##  lkj_corr_cholesky(1)         L                                       
##  lkj_corr_cholesky(1)         L                                       
##  student_t(3, 0, 2.5)        sd                                       
##  student_t(3, 0, 2.5)        sd                                       
##  student_t(3, 0, 2.5)        sd                              Intercept
##  student_t(3, 0, 2.5)        sd                   other_contribution_c
##  student_t(3, 0, 2.5)        sd                      subclusterConc_an
##  student_t(3, 0, 2.5)        sd subclusterConc_an:other_contribution_c
##  student_t(3, 0, 2.5)        sd                      subclusterConc_in
##  student_t(3, 0, 2.5)        sd subclusterConc_in:other_contribution_c
##  student_t(3, 0, 2.5)        sd                           subclusterEM
##  student_t(3, 0, 2.5)        sd      subclusterEM:other_contribution_c
##  student_t(3, 0, 2.5)        sd                           subclusterPS
##  student_t(3, 0, 2.5)        sd      subclusterPS:other_contribution_c
##  student_t(3, 0, 2.5)        sd                           subclusterSS
##  student_t(3, 0, 2.5)        sd      subclusterSS:other_contribution_c
##  student_t(3, 0, 2.5)        sd                                       
##  student_t(3, 0, 2.5)        sd                              Intercept
##  student_t(3, 0, 2.5)        sd                   other_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##                    phi                  default
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)

Check posterior predictive checks of the mixed beta regression:

pp_check(subcluster_dist_mdl, ndraws = 100)

Check this model:

subcluster_dist_mdl
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: closeness_01 ~ 1 + subcluster + other_contribution_c + difficulty_c + subcluster:other_contribution_c + (1 + subcluster + other_contribution_c + subcluster:other_contribution_c | participant) + (1 + other_contribution_c | word) 
##          phi ~ 1
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                                    Estimate
## sd(Intercept)                                                                          0.86
## sd(subclusterConc_an)                                                                  0.42
## sd(subclusterConc_in)                                                                  0.30
## sd(subclusterEM)                                                                       0.09
## sd(subclusterPS)                                                                       0.27
## sd(subclusterSS)                                                                       0.12
## sd(other_contribution_c)                                                               0.02
## sd(subclusterConc_an:other_contribution_c)                                             0.02
## sd(subclusterConc_in:other_contribution_c)                                             0.02
## sd(subclusterEM:other_contribution_c)                                                  0.01
## sd(subclusterPS:other_contribution_c)                                                  0.02
## sd(subclusterSS:other_contribution_c)                                                  0.01
## cor(Intercept,subclusterConc_an)                                                      -0.03
## cor(Intercept,subclusterConc_in)                                                      -0.05
## cor(subclusterConc_an,subclusterConc_in)                                               0.67
## cor(Intercept,subclusterEM)                                                           -0.00
## cor(subclusterConc_an,subclusterEM)                                                    0.03
## cor(subclusterConc_in,subclusterEM)                                                    0.03
## cor(Intercept,subclusterPS)                                                            0.00
## cor(subclusterConc_an,subclusterPS)                                                   -0.11
## cor(subclusterConc_in,subclusterPS)                                                   -0.03
## cor(subclusterEM,subclusterPS)                                                         0.02
## cor(Intercept,subclusterSS)                                                            0.07
## cor(subclusterConc_an,subclusterSS)                                                    0.02
## cor(subclusterConc_in,subclusterSS)                                                   -0.02
## cor(subclusterEM,subclusterSS)                                                         0.04
## cor(subclusterPS,subclusterSS)                                                         0.04
## cor(Intercept,other_contribution_c)                                                   -0.01
## cor(subclusterConc_an,other_contribution_c)                                            0.10
## cor(subclusterConc_in,other_contribution_c)                                           -0.02
## cor(subclusterEM,other_contribution_c)                                                 0.02
## cor(subclusterPS,other_contribution_c)                                                -0.11
## cor(subclusterSS,other_contribution_c)                                                -0.10
## cor(Intercept,subclusterConc_an:other_contribution_c)                                  0.14
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                         -0.27
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                         -0.07
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                              -0.01
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                              -0.03
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                               0.08
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                      -0.30
## cor(Intercept,subclusterConc_in:other_contribution_c)                                 -0.01
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                          0.03
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                          0.12
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                               0.00
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                              -0.11
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                               0.15
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                      -0.37
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)     0.54
## cor(Intercept,subclusterEM:other_contribution_c)                                       0.12
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                               0.02
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                               0.03
## cor(subclusterEM,subclusterEM:other_contribution_c)                                    0.09
## cor(subclusterPS,subclusterEM:other_contribution_c)                                   -0.08
## cor(subclusterSS,subclusterEM:other_contribution_c)                                   -0.10
## cor(other_contribution_c,subclusterEM:other_contribution_c)                            0.01
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)          0.01
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)          0.07
## cor(Intercept,subclusterPS:other_contribution_c)                                       0.06
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                              -0.10
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                              -0.07
## cor(subclusterEM,subclusterPS:other_contribution_c)                                   -0.02
## cor(subclusterPS,subclusterPS:other_contribution_c)                                    0.33
## cor(subclusterSS,subclusterPS:other_contribution_c)                                    0.05
## cor(other_contribution_c,subclusterPS:other_contribution_c)                           -0.00
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)         -0.11
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)         -0.11
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)              -0.05
## cor(Intercept,subclusterSS:other_contribution_c)                                      -0.10
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                               0.14
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                               0.13
## cor(subclusterEM,subclusterSS:other_contribution_c)                                   -0.00
## cor(subclusterPS,subclusterSS:other_contribution_c)                                    0.02
## cor(subclusterSS,subclusterSS:other_contribution_c)                                    0.02
## cor(other_contribution_c,subclusterSS:other_contribution_c)                            0.05
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)          0.00
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)          0.08
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)               0.05
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)               0.13
##                                                                                    Est.Error
## sd(Intercept)                                                                           0.07
## sd(subclusterConc_an)                                                                   0.15
## sd(subclusterConc_in)                                                                   0.15
## sd(subclusterEM)                                                                        0.07
## sd(subclusterPS)                                                                        0.13
## sd(subclusterSS)                                                                        0.08
## sd(other_contribution_c)                                                                0.00
## sd(subclusterConc_an:other_contribution_c)                                              0.01
## sd(subclusterConc_in:other_contribution_c)                                              0.01
## sd(subclusterEM:other_contribution_c)                                                   0.00
## sd(subclusterPS:other_contribution_c)                                                   0.01
## sd(subclusterSS:other_contribution_c)                                                   0.00
## cor(Intercept,subclusterConc_an)                                                        0.17
## cor(Intercept,subclusterConc_in)                                                        0.19
## cor(subclusterConc_an,subclusterConc_in)                                                0.31
## cor(Intercept,subclusterEM)                                                             0.26
## cor(subclusterConc_an,subclusterEM)                                                     0.27
## cor(subclusterConc_in,subclusterEM)                                                     0.27
## cor(Intercept,subclusterPS)                                                             0.21
## cor(subclusterConc_an,subclusterPS)                                                     0.24
## cor(subclusterConc_in,subclusterPS)                                                     0.25
## cor(subclusterEM,subclusterPS)                                                          0.28
## cor(Intercept,subclusterSS)                                                             0.25
## cor(subclusterConc_an,subclusterSS)                                                     0.26
## cor(subclusterConc_in,subclusterSS)                                                     0.26
## cor(subclusterEM,subclusterSS)                                                          0.27
## cor(subclusterPS,subclusterSS)                                                          0.28
## cor(Intercept,other_contribution_c)                                                     0.13
## cor(subclusterConc_an,other_contribution_c)                                             0.17
## cor(subclusterConc_in,other_contribution_c)                                             0.20
## cor(subclusterEM,other_contribution_c)                                                  0.26
## cor(subclusterPS,other_contribution_c)                                                  0.22
## cor(subclusterSS,other_contribution_c)                                                  0.26
## cor(Intercept,subclusterConc_an:other_contribution_c)                                   0.18
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                           0.19
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                           0.22
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                                0.27
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                                0.25
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                                0.27
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                        0.23
## cor(Intercept,subclusterConc_in:other_contribution_c)                                   0.18
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                           0.26
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                           0.23
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                                0.26
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                                0.25
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                                0.27
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                        0.24
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)      0.34
## cor(Intercept,subclusterEM:other_contribution_c)                                        0.18
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                                0.22
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                                0.23
## cor(subclusterEM,subclusterEM:other_contribution_c)                                     0.27
## cor(subclusterPS,subclusterEM:other_contribution_c)                                     0.24
## cor(subclusterSS,subclusterEM:other_contribution_c)                                     0.27
## cor(other_contribution_c,subclusterEM:other_contribution_c)                             0.22
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)           0.24
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)           0.23
## cor(Intercept,subclusterPS:other_contribution_c)                                        0.16
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                                0.20
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                                0.23
## cor(subclusterEM,subclusterPS:other_contribution_c)                                     0.27
## cor(subclusterPS,subclusterPS:other_contribution_c)                                     0.23
## cor(subclusterSS,subclusterPS:other_contribution_c)                                     0.27
## cor(other_contribution_c,subclusterPS:other_contribution_c)                             0.19
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)           0.21
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)           0.22
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)                0.21
## cor(Intercept,subclusterSS:other_contribution_c)                                        0.25
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                                0.28
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                                0.28
## cor(subclusterEM,subclusterSS:other_contribution_c)                                     0.28
## cor(subclusterPS,subclusterSS:other_contribution_c)                                     0.27
## cor(subclusterSS,subclusterSS:other_contribution_c)                                     0.27
## cor(other_contribution_c,subclusterSS:other_contribution_c)                             0.27
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)           0.28
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)           0.27
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)                0.27
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)                0.28
##                                                                                    l-95% CI
## sd(Intercept)                                                                          0.74
## sd(subclusterConc_an)                                                                  0.12
## sd(subclusterConc_in)                                                                  0.01
## sd(subclusterEM)                                                                       0.00
## sd(subclusterPS)                                                                       0.03
## sd(subclusterSS)                                                                       0.01
## sd(other_contribution_c)                                                               0.01
## sd(subclusterConc_an:other_contribution_c)                                             0.00
## sd(subclusterConc_in:other_contribution_c)                                             0.00
## sd(subclusterEM:other_contribution_c)                                                  0.01
## sd(subclusterPS:other_contribution_c)                                                  0.01
## sd(subclusterSS:other_contribution_c)                                                  0.00
## cor(Intercept,subclusterConc_an)                                                      -0.31
## cor(Intercept,subclusterConc_in)                                                      -0.38
## cor(subclusterConc_an,subclusterConc_in)                                              -0.18
## cor(Intercept,subclusterEM)                                                           -0.49
## cor(subclusterConc_an,subclusterEM)                                                   -0.50
## cor(subclusterConc_in,subclusterEM)                                                   -0.50
## cor(Intercept,subclusterPS)                                                           -0.41
## cor(subclusterConc_an,subclusterPS)                                                   -0.56
## cor(subclusterConc_in,subclusterPS)                                                   -0.51
## cor(subclusterEM,subclusterPS)                                                        -0.53
## cor(Intercept,subclusterSS)                                                           -0.43
## cor(subclusterConc_an,subclusterSS)                                                   -0.48
## cor(subclusterConc_in,subclusterSS)                                                   -0.52
## cor(subclusterEM,subclusterSS)                                                        -0.50
## cor(subclusterPS,subclusterSS)                                                        -0.50
## cor(Intercept,other_contribution_c)                                                   -0.27
## cor(subclusterConc_an,other_contribution_c)                                           -0.22
## cor(subclusterConc_in,other_contribution_c)                                           -0.42
## cor(subclusterEM,other_contribution_c)                                                -0.49
## cor(subclusterPS,other_contribution_c)                                                -0.53
## cor(subclusterSS,other_contribution_c)                                                -0.57
## cor(Intercept,subclusterConc_an:other_contribution_c)                                 -0.21
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                         -0.61
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                         -0.48
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                              -0.52
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                              -0.50
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                              -0.47
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                      -0.64
## cor(Intercept,subclusterConc_in:other_contribution_c)                                 -0.42
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                         -0.46
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                         -0.37
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                              -0.50
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                              -0.56
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                              -0.42
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                      -0.70
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)    -0.28
## cor(Intercept,subclusterEM:other_contribution_c)                                      -0.24
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                              -0.40
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                              -0.42
## cor(subclusterEM,subclusterEM:other_contribution_c)                                   -0.45
## cor(subclusterPS,subclusterEM:other_contribution_c)                                   -0.53
## cor(subclusterSS,subclusterEM:other_contribution_c)                                   -0.60
## cor(other_contribution_c,subclusterEM:other_contribution_c)                           -0.42
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)         -0.46
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)         -0.41
## cor(Intercept,subclusterPS:other_contribution_c)                                      -0.24
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                              -0.48
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                              -0.49
## cor(subclusterEM,subclusterPS:other_contribution_c)                                   -0.54
## cor(subclusterPS,subclusterPS:other_contribution_c)                                   -0.18
## cor(subclusterSS,subclusterPS:other_contribution_c)                                   -0.49
## cor(other_contribution_c,subclusterPS:other_contribution_c)                           -0.37
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)         -0.52
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)         -0.53
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)              -0.46
## cor(Intercept,subclusterSS:other_contribution_c)                                      -0.56
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                              -0.43
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                              -0.45
## cor(subclusterEM,subclusterSS:other_contribution_c)                                   -0.53
## cor(subclusterPS,subclusterSS:other_contribution_c)                                   -0.51
## cor(subclusterSS,subclusterSS:other_contribution_c)                                   -0.51
## cor(other_contribution_c,subclusterSS:other_contribution_c)                           -0.49
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)         -0.52
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)         -0.45
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)              -0.48
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)              -0.45
##                                                                                    u-95% CI
## sd(Intercept)                                                                          0.99
## sd(subclusterConc_an)                                                                  0.65
## sd(subclusterConc_in)                                                                  0.52
## sd(subclusterEM)                                                                       0.26
## sd(subclusterPS)                                                                       0.54
## sd(subclusterSS)                                                                       0.29
## sd(other_contribution_c)                                                               0.03
## sd(subclusterConc_an:other_contribution_c)                                             0.03
## sd(subclusterConc_in:other_contribution_c)                                             0.03
## sd(subclusterEM:other_contribution_c)                                                  0.02
## sd(subclusterPS:other_contribution_c)                                                  0.04
## sd(subclusterSS:other_contribution_c)                                                  0.02
## cor(Intercept,subclusterConc_an)                                                       0.35
## cor(Intercept,subclusterConc_in)                                                       0.38
## cor(subclusterConc_an,subclusterConc_in)                                               0.94
## cor(Intercept,subclusterEM)                                                            0.51
## cor(subclusterConc_an,subclusterEM)                                                    0.54
## cor(subclusterConc_in,subclusterEM)                                                    0.54
## cor(Intercept,subclusterPS)                                                            0.43
## cor(subclusterConc_an,subclusterPS)                                                    0.38
## cor(subclusterConc_in,subclusterPS)                                                    0.47
## cor(subclusterEM,subclusterPS)                                                         0.55
## cor(Intercept,subclusterSS)                                                            0.54
## cor(subclusterConc_an,subclusterSS)                                                    0.51
## cor(subclusterConc_in,subclusterSS)                                                    0.49
## cor(subclusterEM,subclusterSS)                                                         0.56
## cor(subclusterPS,subclusterSS)                                                         0.55
## cor(Intercept,other_contribution_c)                                                    0.25
## cor(subclusterConc_an,other_contribution_c)                                            0.44
## cor(subclusterConc_in,other_contribution_c)                                            0.37
## cor(subclusterEM,other_contribution_c)                                                 0.51
## cor(subclusterPS,other_contribution_c)                                                 0.35
## cor(subclusterSS,other_contribution_c)                                                 0.45
## cor(Intercept,subclusterConc_an:other_contribution_c)                                  0.51
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                          0.14
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                          0.37
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                               0.50
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                               0.47
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                               0.57
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                       0.25
## cor(Intercept,subclusterConc_in:other_contribution_c)                                  0.32
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                          0.54
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                          0.56
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                               0.51
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                               0.42
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                               0.62
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                       0.21
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)     0.91
## cor(Intercept,subclusterEM:other_contribution_c)                                       0.46
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                               0.45
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                               0.48
## cor(subclusterEM,subclusterEM:other_contribution_c)                                    0.59
## cor(subclusterPS,subclusterEM:other_contribution_c)                                    0.41
## cor(subclusterSS,subclusterEM:other_contribution_c)                                    0.43
## cor(other_contribution_c,subclusterEM:other_contribution_c)                            0.45
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)          0.47
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)          0.48
## cor(Intercept,subclusterPS:other_contribution_c)                                       0.40
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                               0.32
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                               0.43
## cor(subclusterEM,subclusterPS:other_contribution_c)                                    0.51
## cor(subclusterPS,subclusterPS:other_contribution_c)                                    0.71
## cor(subclusterSS,subclusterPS:other_contribution_c)                                    0.56
## cor(other_contribution_c,subclusterPS:other_contribution_c)                            0.38
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)          0.35
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)          0.33
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)               0.36
## cor(Intercept,subclusterSS:other_contribution_c)                                       0.42
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                               0.64
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                               0.63
## cor(subclusterEM,subclusterSS:other_contribution_c)                                    0.53
## cor(subclusterPS,subclusterSS:other_contribution_c)                                    0.54
## cor(subclusterSS,subclusterSS:other_contribution_c)                                    0.54
## cor(other_contribution_c,subclusterSS:other_contribution_c)                            0.55
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)          0.53
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)          0.58
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)               0.55
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)               0.64
##                                                                                    Rhat
## sd(Intercept)                                                                      1.00
## sd(subclusterConc_an)                                                              1.01
## sd(subclusterConc_in)                                                              1.02
## sd(subclusterEM)                                                                   1.00
## sd(subclusterPS)                                                                   1.01
## sd(subclusterSS)                                                                   1.00
## sd(other_contribution_c)                                                           1.01
## sd(subclusterConc_an:other_contribution_c)                                         1.02
## sd(subclusterConc_in:other_contribution_c)                                         1.02
## sd(subclusterEM:other_contribution_c)                                              1.00
## sd(subclusterPS:other_contribution_c)                                              1.01
## sd(subclusterSS:other_contribution_c)                                              1.00
## cor(Intercept,subclusterConc_an)                                                   1.01
## cor(Intercept,subclusterConc_in)                                                   1.01
## cor(subclusterConc_an,subclusterConc_in)                                           1.01
## cor(Intercept,subclusterEM)                                                        1.00
## cor(subclusterConc_an,subclusterEM)                                                1.00
## cor(subclusterConc_in,subclusterEM)                                                1.00
## cor(Intercept,subclusterPS)                                                        1.00
## cor(subclusterConc_an,subclusterPS)                                                1.00
## cor(subclusterConc_in,subclusterPS)                                                1.00
## cor(subclusterEM,subclusterPS)                                                     1.00
## cor(Intercept,subclusterSS)                                                        1.00
## cor(subclusterConc_an,subclusterSS)                                                1.00
## cor(subclusterConc_in,subclusterSS)                                                1.00
## cor(subclusterEM,subclusterSS)                                                     1.00
## cor(subclusterPS,subclusterSS)                                                     1.00
## cor(Intercept,other_contribution_c)                                                1.00
## cor(subclusterConc_an,other_contribution_c)                                        1.00
## cor(subclusterConc_in,other_contribution_c)                                        1.01
## cor(subclusterEM,other_contribution_c)                                             1.01
## cor(subclusterPS,other_contribution_c)                                             1.00
## cor(subclusterSS,other_contribution_c)                                             1.01
## cor(Intercept,subclusterConc_an:other_contribution_c)                              1.00
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                      1.00
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                      1.00
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                           1.00
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                           1.00
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                           1.00
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                   1.01
## cor(Intercept,subclusterConc_in:other_contribution_c)                              1.00
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                      1.01
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                      1.00
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                           1.00
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                           1.00
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                           1.00
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                   1.01
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 1.02
## cor(Intercept,subclusterEM:other_contribution_c)                                   1.00
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                           1.00
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                           1.00
## cor(subclusterEM,subclusterEM:other_contribution_c)                                1.00
## cor(subclusterPS,subclusterEM:other_contribution_c)                                1.00
## cor(subclusterSS,subclusterEM:other_contribution_c)                                1.00
## cor(other_contribution_c,subclusterEM:other_contribution_c)                        1.00
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)      1.00
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)      1.00
## cor(Intercept,subclusterPS:other_contribution_c)                                   1.00
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                           1.00
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                           1.00
## cor(subclusterEM,subclusterPS:other_contribution_c)                                1.00
## cor(subclusterPS,subclusterPS:other_contribution_c)                                1.00
## cor(subclusterSS,subclusterPS:other_contribution_c)                                1.00
## cor(other_contribution_c,subclusterPS:other_contribution_c)                        1.00
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)      1.00
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)      1.00
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)           1.00
## cor(Intercept,subclusterSS:other_contribution_c)                                   1.00
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                           1.00
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                           1.00
## cor(subclusterEM,subclusterSS:other_contribution_c)                                1.00
## cor(subclusterPS,subclusterSS:other_contribution_c)                                1.00
## cor(subclusterSS,subclusterSS:other_contribution_c)                                1.00
## cor(other_contribution_c,subclusterSS:other_contribution_c)                        1.00
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)      1.00
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)      1.00
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)           1.00
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)           1.00
##                                                                                    Bulk_ESS
## sd(Intercept)                                                                          2202
## sd(subclusterConc_an)                                                                   148
## sd(subclusterConc_in)                                                                   146
## sd(subclusterEM)                                                                       1548
## sd(subclusterPS)                                                                        590
## sd(subclusterSS)                                                                       1303
## sd(other_contribution_c)                                                                261
## sd(subclusterConc_an:other_contribution_c)                                              139
## sd(subclusterConc_in:other_contribution_c)                                              142
## sd(subclusterEM:other_contribution_c)                                                  1375
## sd(subclusterPS:other_contribution_c)                                                   687
## sd(subclusterSS:other_contribution_c)                                                  1468
## cor(Intercept,subclusterConc_an)                                                        429
## cor(Intercept,subclusterConc_in)                                                        911
## cor(subclusterConc_an,subclusterConc_in)                                                177
## cor(Intercept,subclusterEM)                                                           12310
## cor(subclusterConc_an,subclusterEM)                                                    6739
## cor(subclusterConc_in,subclusterEM)                                                    6052
## cor(Intercept,subclusterPS)                                                            2748
## cor(subclusterConc_an,subclusterPS)                                                    3143
## cor(subclusterConc_in,subclusterPS)                                                    3174
## cor(subclusterEM,subclusterPS)                                                         2351
## cor(Intercept,subclusterSS)                                                           10881
## cor(subclusterConc_an,subclusterSS)                                                    7355
## cor(subclusterConc_in,subclusterSS)                                                    8726
## cor(subclusterEM,subclusterSS)                                                         6000
## cor(subclusterPS,subclusterSS)                                                         7686
## cor(Intercept,other_contribution_c)                                                    3198
## cor(subclusterConc_an,other_contribution_c)                                            1740
## cor(subclusterConc_in,other_contribution_c)                                            1183
## cor(subclusterEM,other_contribution_c)                                                  931
## cor(subclusterPS,other_contribution_c)                                                 1131
## cor(subclusterSS,other_contribution_c)                                                  687
## cor(Intercept,subclusterConc_an:other_contribution_c)                                  3222
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                          1304
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                          1974
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                               1947
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                               2288
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                                801
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                        429
## cor(Intercept,subclusterConc_in:other_contribution_c)                                  2601
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                           281
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                           694
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                               1924
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                               2483
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                                847
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                        332
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)      166
## cor(Intercept,subclusterEM:other_contribution_c)                                       5439
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                               3743
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                               3401
## cor(subclusterEM,subclusterEM:other_contribution_c)                                    2021
## cor(subclusterPS,subclusterEM:other_contribution_c)                                    3222
## cor(subclusterSS,subclusterEM:other_contribution_c)                                    2698
## cor(other_contribution_c,subclusterEM:other_contribution_c)                            1210
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)          4227
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)          4025
## cor(Intercept,subclusterPS:other_contribution_c)                                       4028
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                               2037
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                               1336
## cor(subclusterEM,subclusterPS:other_contribution_c)                                    1338
## cor(subclusterPS,subclusterPS:other_contribution_c)                                    1308
## cor(subclusterSS,subclusterPS:other_contribution_c)                                    1956
## cor(other_contribution_c,subclusterPS:other_contribution_c)                            3603
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)          2553
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)          3216
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)               4677
## cor(Intercept,subclusterSS:other_contribution_c)                                       4547
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                               1286
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                               1443
## cor(subclusterEM,subclusterSS:other_contribution_c)                                    7037
## cor(subclusterPS,subclusterSS:other_contribution_c)                                    8321
## cor(subclusterSS,subclusterSS:other_contribution_c)                                    7729
## cor(other_contribution_c,subclusterSS:other_contribution_c)                            2129
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)          2614
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)          7762
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)               8068
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)               6222
##                                                                                    Tail_ESS
## sd(Intercept)                                                                          4597
## sd(subclusterConc_an)                                                                   774
## sd(subclusterConc_in)                                                                   801
## sd(subclusterEM)                                                                       2517
## sd(subclusterPS)                                                                       1261
## sd(subclusterSS)                                                                       4174
## sd(other_contribution_c)                                                               1977
## sd(subclusterConc_an:other_contribution_c)                                              883
## sd(subclusterConc_in:other_contribution_c)                                             1011
## sd(subclusterEM:other_contribution_c)                                                  1040
## sd(subclusterPS:other_contribution_c)                                                  1138
## sd(subclusterSS:other_contribution_c)                                                  5117
## cor(Intercept,subclusterConc_an)                                                       1074
## cor(Intercept,subclusterConc_in)                                                       1203
## cor(subclusterConc_an,subclusterConc_in)                                                762
## cor(Intercept,subclusterEM)                                                            8500
## cor(subclusterConc_an,subclusterEM)                                                    7817
## cor(subclusterConc_in,subclusterEM)                                                    8436
## cor(Intercept,subclusterPS)                                                            4972
## cor(subclusterConc_an,subclusterPS)                                                    4996
## cor(subclusterConc_in,subclusterPS)                                                    4094
## cor(subclusterEM,subclusterPS)                                                         4232
## cor(Intercept,subclusterSS)                                                            7739
## cor(subclusterConc_an,subclusterSS)                                                    7340
## cor(subclusterConc_in,subclusterSS)                                                    8472
## cor(subclusterEM,subclusterSS)                                                         8496
## cor(subclusterPS,subclusterSS)                                                         8694
## cor(Intercept,other_contribution_c)                                                    6449
## cor(subclusterConc_an,other_contribution_c)                                            2466
## cor(subclusterConc_in,other_contribution_c)                                            1292
## cor(subclusterEM,other_contribution_c)                                                 2010
## cor(subclusterPS,other_contribution_c)                                                 2037
## cor(subclusterSS,other_contribution_c)                                                 1343
## cor(Intercept,subclusterConc_an:other_contribution_c)                                  2783
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c)                          2792
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c)                          2935
## cor(subclusterEM,subclusterConc_an:other_contribution_c)                               3426
## cor(subclusterPS,subclusterConc_an:other_contribution_c)                               3494
## cor(subclusterSS,subclusterConc_an:other_contribution_c)                               3667
## cor(other_contribution_c,subclusterConc_an:other_contribution_c)                       1466
## cor(Intercept,subclusterConc_in:other_contribution_c)                                  2186
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c)                          1046
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c)                          1477
## cor(subclusterEM,subclusterConc_in:other_contribution_c)                               3525
## cor(subclusterPS,subclusterConc_in:other_contribution_c)                               3654
## cor(subclusterSS,subclusterConc_in:other_contribution_c)                               3399
## cor(other_contribution_c,subclusterConc_in:other_contribution_c)                       1473
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c)     1270
## cor(Intercept,subclusterEM:other_contribution_c)                                       8165
## cor(subclusterConc_an,subclusterEM:other_contribution_c)                               3837
## cor(subclusterConc_in,subclusterEM:other_contribution_c)                               4802
## cor(subclusterEM,subclusterEM:other_contribution_c)                                    5214
## cor(subclusterPS,subclusterEM:other_contribution_c)                                    5162
## cor(subclusterSS,subclusterEM:other_contribution_c)                                    4915
## cor(other_contribution_c,subclusterEM:other_contribution_c)                            5830
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c)          6581
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c)          6076
## cor(Intercept,subclusterPS:other_contribution_c)                                       4368
## cor(subclusterConc_an,subclusterPS:other_contribution_c)                               2462
## cor(subclusterConc_in,subclusterPS:other_contribution_c)                               1959
## cor(subclusterEM,subclusterPS:other_contribution_c)                                    2697
## cor(subclusterPS,subclusterPS:other_contribution_c)                                    1831
## cor(subclusterSS,subclusterPS:other_contribution_c)                                    4307
## cor(other_contribution_c,subclusterPS:other_contribution_c)                            6567
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c)          3001
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c)          2901
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)               7174
## cor(Intercept,subclusterSS:other_contribution_c)                                       6790
## cor(subclusterConc_an,subclusterSS:other_contribution_c)                               6208
## cor(subclusterConc_in,subclusterSS:other_contribution_c)                               6786
## cor(subclusterEM,subclusterSS:other_contribution_c)                                    9259
## cor(subclusterPS,subclusterSS:other_contribution_c)                                    9707
## cor(subclusterSS,subclusterSS:other_contribution_c)                                    8821
## cor(other_contribution_c,subclusterSS:other_contribution_c)                            8416
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c)          8839
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c)          9620
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)               9216
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)               7945
## 
## ~word (Number of levels: 32) 
##                                     Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                           0.04      0.02     0.00     0.09 1.00
## sd(other_contribution_c)                0.00      0.00     0.00     0.01 1.00
## cor(Intercept,other_contribution_c)     0.06      0.55    -0.93     0.95 1.00
##                                     Bulk_ESS Tail_ESS
## sd(Intercept)                           2717     4398
## sd(other_contribution_c)                2502     3311
## cor(Intercept,other_contribution_c)     3500     6403
## 
## Population-Level Effects: 
##                                        Estimate Est.Error l-95% CI u-95% CI
## Intercept                                  0.98      0.09     0.81     1.16
## phi_Intercept                              3.73      0.07     3.58     3.87
## subclusterConc_an                         -0.02      0.07    -0.16     0.12
## subclusterConc_in                         -0.05      0.06    -0.17     0.08
## subclusterEM                              -0.05      0.06    -0.17     0.07
## subclusterPS                              -0.01      0.07    -0.15     0.14
## subclusterSS                              -0.08      0.07    -0.22     0.05
## other_contribution_c                       0.02      0.00     0.01     0.03
## difficulty_c                              -0.01      0.00    -0.01    -0.00
## subclusterConc_an:other_contribution_c    -0.00      0.00    -0.01     0.01
## subclusterConc_in:other_contribution_c    -0.00      0.00    -0.01     0.01
## subclusterEM:other_contribution_c         -0.00      0.00    -0.01     0.00
## subclusterPS:other_contribution_c         -0.00      0.00    -0.01     0.00
## subclusterSS:other_contribution_c         -0.00      0.00    -0.01     0.00
##                                        Rhat Bulk_ESS Tail_ESS
## Intercept                              1.00     1166     3455
## phi_Intercept                          1.00     2255     5580
## subclusterConc_an                      1.00     3903     6017
## subclusterConc_in                      1.00     4716     6286
## subclusterEM                           1.00     6072     7471
## subclusterPS                           1.00     4358     6471
## subclusterSS                           1.00     6631     7261
## other_contribution_c                   1.00     1793     5343
## difficulty_c                           1.00    11061    10894
## subclusterConc_an:other_contribution_c 1.00     3372     6252
## subclusterConc_in:other_contribution_c 1.00     1923     5854
## subclusterEM:other_contribution_c      1.00     5995     8197
## subclusterPS:other_contribution_c      1.00     5357     6614
## subclusterSS:other_contribution_c      1.00     6524     7835
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(subcluster_dist_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.01         0    -0.01        0        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_mdl,
           'other_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0     0.02         0     0.01     0.03        Inf
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_mdl,
           'subclusterConc_an:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_a... < 0        0         0    -0.01        0       2.07
##   Post.Prob Star
## 1      0.67     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_mdl,
           'subclusterConc_in:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_i... < 0        0         0    -0.01        0       1.84
##   Post.Prob Star
## 1      0.65     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_mdl,
           'subclusterEM:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:oth... < 0        0         0    -0.01        0        4.6
##   Post.Prob Star
## 1      0.82     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_mdl,
           'subclusterPS:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:oth... < 0        0         0    -0.01        0       5.52
##   Post.Prob Star
## 1      0.85     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_mdl,
           'subclusterSS:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:oth... < 0        0         0    -0.01        0       6.88
##   Post.Prob Star
## 1      0.87     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

14 Subcluster models: self-contribution

Do the main analysis of IOS with difficulty as a covariate predictor, to control for this.

subcluster_self_mdl <- brm(IOS ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        self_contribution_c +
                        difficulty_c +
                        subcluster:self_contribution_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           self_contribution_c +
                           subcluster:self_contribution_c|participant) +
                        (1 + self_contribution_c|word),
           
                      data = df,
                      family = cumulative,
           
                      # MCMC settings:
                               
                      seed = 42,
                      cores = 4,
                      iter = 6000,
                      warmup = 3000,
                      control = list(adapt_delta = 0.99))

# Save model:

save(subcluster_self_mdl,
     file = '../models_E2/subcluster_self_mdl.Rdata')

Load model:

load('../models_E2/subcluster_self_mdl.RData')

Show priors:

prior_summary(subcluster_self_mdl)
##                 prior     class                                  coef
##                (flat)         b                                      
##                (flat)         b                          difficulty_c
##                (flat)         b                   self_contribution_c
##                (flat)         b                     subclusterConc_an
##                (flat)         b subclusterConc_an:self_contribution_c
##                (flat)         b                     subclusterConc_in
##                (flat)         b subclusterConc_in:self_contribution_c
##                (flat)         b                          subclusterEM
##                (flat)         b      subclusterEM:self_contribution_c
##                (flat)         b                          subclusterPS
##                (flat)         b      subclusterPS:self_contribution_c
##                (flat)         b                          subclusterSS
##                (flat)         b      subclusterSS:self_contribution_c
##  student_t(3, 0, 2.5) Intercept                                      
##  student_t(3, 0, 2.5) Intercept                                     1
##  student_t(3, 0, 2.5) Intercept                                     2
##  student_t(3, 0, 2.5) Intercept                                     3
##  student_t(3, 0, 2.5) Intercept                                     4
##  student_t(3, 0, 2.5) Intercept                                     5
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                   self_contribution_c
##  student_t(3, 0, 2.5)        sd                     subclusterConc_an
##  student_t(3, 0, 2.5)        sd subclusterConc_an:self_contribution_c
##  student_t(3, 0, 2.5)        sd                     subclusterConc_in
##  student_t(3, 0, 2.5)        sd subclusterConc_in:self_contribution_c
##  student_t(3, 0, 2.5)        sd                          subclusterEM
##  student_t(3, 0, 2.5)        sd      subclusterEM:self_contribution_c
##  student_t(3, 0, 2.5)        sd                          subclusterPS
##  student_t(3, 0, 2.5)        sd      subclusterPS:self_contribution_c
##  student_t(3, 0, 2.5)        sd                          subclusterSS
##  student_t(3, 0, 2.5)        sd      subclusterSS:self_contribution_c
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                   self_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)

Check posterior predictive checks of the mixed beta regression:

pp_check(subcluster_self_mdl, ndraws = 100)

Check this model:

subcluster_self_mdl
##  Family: cumulative 
##   Links: mu = logit; disc = identity 
## Formula: IOS ~ 1 + subcluster + self_contribution_c + difficulty_c + subcluster:self_contribution_c + (1 + subcluster + self_contribution_c + subcluster:self_contribution_c | participant) + (1 + self_contribution_c | word) 
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                                  Estimate
## sd(Intercept)                                                                        2.90
## sd(subclusterConc_an)                                                                1.71
## sd(subclusterConc_in)                                                                1.94
## sd(subclusterEM)                                                                     0.45
## sd(subclusterPS)                                                                     1.03
## sd(subclusterSS)                                                                     0.49
## sd(self_contribution_c)                                                              0.06
## sd(subclusterConc_an:self_contribution_c)                                            0.03
## sd(subclusterConc_in:self_contribution_c)                                            0.03
## sd(subclusterEM:self_contribution_c)                                                 0.04
## sd(subclusterPS:self_contribution_c)                                                 0.03
## sd(subclusterSS:self_contribution_c)                                                 0.04
## cor(Intercept,subclusterConc_an)                                                    -0.18
## cor(Intercept,subclusterConc_in)                                                    -0.16
## cor(subclusterConc_an,subclusterConc_in)                                             0.78
## cor(Intercept,subclusterEM)                                                          0.00
## cor(subclusterConc_an,subclusterEM)                                                 -0.05
## cor(subclusterConc_in,subclusterEM)                                                 -0.07
## cor(Intercept,subclusterPS)                                                          0.00
## cor(subclusterConc_an,subclusterPS)                                                 -0.23
## cor(subclusterConc_in,subclusterPS)                                                 -0.24
## cor(subclusterEM,subclusterPS)                                                       0.06
## cor(Intercept,subclusterSS)                                                          0.03
## cor(subclusterConc_an,subclusterSS)                                                 -0.02
## cor(subclusterConc_in,subclusterSS)                                                  0.00
## cor(subclusterEM,subclusterSS)                                                       0.02
## cor(subclusterPS,subclusterSS)                                                       0.05
## cor(Intercept,self_contribution_c)                                                   0.19
## cor(subclusterConc_an,self_contribution_c)                                          -0.13
## cor(subclusterConc_in,self_contribution_c)                                          -0.17
## cor(subclusterEM,self_contribution_c)                                               -0.02
## cor(subclusterPS,self_contribution_c)                                                0.24
## cor(subclusterSS,self_contribution_c)                                                0.08
## cor(Intercept,subclusterConc_an:self_contribution_c)                                 0.10
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                         0.04
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                         0.00
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                              0.00
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                              0.03
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                              0.01
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                       0.16
## cor(Intercept,subclusterConc_in:self_contribution_c)                                 0.06
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                         0.08
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                         0.13
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                             -0.07
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                              0.09
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                              0.01
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                      -0.03
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)     0.15
## cor(Intercept,subclusterEM:self_contribution_c)                                      0.04
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                             -0.01
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                             -0.04
## cor(subclusterEM,subclusterEM:self_contribution_c)                                   0.05
## cor(subclusterPS,subclusterEM:self_contribution_c)                                  -0.13
## cor(subclusterSS,subclusterEM:self_contribution_c)                                   0.01
## cor(self_contribution_c,subclusterEM:self_contribution_c)                           -0.24
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)         -0.01
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)         -0.08
## cor(Intercept,subclusterPS:self_contribution_c)                                      0.02
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                             -0.03
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                              0.02
## cor(subclusterEM,subclusterPS:self_contribution_c)                                  -0.03
## cor(subclusterPS,subclusterPS:self_contribution_c)                                   0.04
## cor(subclusterSS,subclusterPS:self_contribution_c)                                   0.00
## cor(self_contribution_c,subclusterPS:self_contribution_c)                            0.02
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)         -0.01
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)          0.03
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)               0.01
## cor(Intercept,subclusterSS:self_contribution_c)                                      0.02
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                             -0.08
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                             -0.14
## cor(subclusterEM,subclusterSS:self_contribution_c)                                   0.02
## cor(subclusterPS,subclusterSS:self_contribution_c)                                   0.01
## cor(subclusterSS,subclusterSS:self_contribution_c)                                  -0.03
## cor(self_contribution_c,subclusterSS:self_contribution_c)                           -0.02
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)         -0.00
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)         -0.05
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)               0.02
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)               0.01
##                                                                                  Est.Error
## sd(Intercept)                                                                         0.27
## sd(subclusterConc_an)                                                                 0.31
## sd(subclusterConc_in)                                                                 0.30
## sd(subclusterEM)                                                                      0.33
## sd(subclusterPS)                                                                      0.47
## sd(subclusterSS)                                                                      0.37
## sd(self_contribution_c)                                                               0.01
## sd(subclusterConc_an:self_contribution_c)                                             0.02
## sd(subclusterConc_in:self_contribution_c)                                             0.02
## sd(subclusterEM:self_contribution_c)                                                  0.02
## sd(subclusterPS:self_contribution_c)                                                  0.02
## sd(subclusterSS:self_contribution_c)                                                  0.03
## cor(Intercept,subclusterConc_an)                                                      0.14
## cor(Intercept,subclusterConc_in)                                                      0.13
## cor(subclusterConc_an,subclusterConc_in)                                              0.09
## cor(Intercept,subclusterEM)                                                           0.26
## cor(subclusterConc_an,subclusterEM)                                                   0.27
## cor(subclusterConc_in,subclusterEM)                                                   0.26
## cor(Intercept,subclusterPS)                                                           0.21
## cor(subclusterConc_an,subclusterPS)                                                   0.22
## cor(subclusterConc_in,subclusterPS)                                                   0.22
## cor(subclusterEM,subclusterPS)                                                        0.27
## cor(Intercept,subclusterSS)                                                           0.26
## cor(subclusterConc_an,subclusterSS)                                                   0.26
## cor(subclusterConc_in,subclusterSS)                                                   0.26
## cor(subclusterEM,subclusterSS)                                                        0.28
## cor(subclusterPS,subclusterSS)                                                        0.28
## cor(Intercept,self_contribution_c)                                                    0.16
## cor(subclusterConc_an,self_contribution_c)                                            0.19
## cor(subclusterConc_in,self_contribution_c)                                            0.18
## cor(subclusterEM,self_contribution_c)                                                 0.27
## cor(subclusterPS,self_contribution_c)                                                 0.24
## cor(subclusterSS,self_contribution_c)                                                 0.27
## cor(Intercept,subclusterConc_an:self_contribution_c)                                  0.24
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                          0.24
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                          0.24
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                               0.28
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                               0.27
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                               0.28
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                        0.26
## cor(Intercept,subclusterConc_in:self_contribution_c)                                  0.24
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                          0.25
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                          0.25
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                               0.28
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                               0.27
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                               0.28
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                        0.26
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)      0.29
## cor(Intercept,subclusterEM:self_contribution_c)                                       0.24
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                               0.24
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                               0.24
## cor(subclusterEM,subclusterEM:self_contribution_c)                                    0.27
## cor(subclusterPS,subclusterEM:self_contribution_c)                                    0.27
## cor(subclusterSS,subclusterEM:self_contribution_c)                                    0.28
## cor(self_contribution_c,subclusterEM:self_contribution_c)                             0.27
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)           0.27
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)           0.27
## cor(Intercept,subclusterPS:self_contribution_c)                                       0.25
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                               0.26
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                               0.26
## cor(subclusterEM,subclusterPS:self_contribution_c)                                    0.28
## cor(subclusterPS,subclusterPS:self_contribution_c)                                    0.27
## cor(subclusterSS,subclusterPS:self_contribution_c)                                    0.28
## cor(self_contribution_c,subclusterPS:self_contribution_c)                             0.27
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)           0.27
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)           0.28
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)                0.27
## cor(Intercept,subclusterSS:self_contribution_c)                                       0.23
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                               0.25
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                               0.25
## cor(subclusterEM,subclusterSS:self_contribution_c)                                    0.28
## cor(subclusterPS,subclusterSS:self_contribution_c)                                    0.27
## cor(subclusterSS,subclusterSS:self_contribution_c)                                    0.28
## cor(self_contribution_c,subclusterSS:self_contribution_c)                             0.27
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)           0.27
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)           0.27
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)                0.27
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)                0.28
##                                                                                  l-95% CI
## sd(Intercept)                                                                        2.40
## sd(subclusterConc_an)                                                                1.11
## sd(subclusterConc_in)                                                                1.36
## sd(subclusterEM)                                                                     0.02
## sd(subclusterPS)                                                                     0.10
## sd(subclusterSS)                                                                     0.02
## sd(self_contribution_c)                                                              0.03
## sd(subclusterConc_an:self_contribution_c)                                            0.00
## sd(subclusterConc_in:self_contribution_c)                                            0.00
## sd(subclusterEM:self_contribution_c)                                                 0.00
## sd(subclusterPS:self_contribution_c)                                                 0.00
## sd(subclusterSS:self_contribution_c)                                                 0.00
## cor(Intercept,subclusterConc_an)                                                    -0.44
## cor(Intercept,subclusterConc_in)                                                    -0.40
## cor(subclusterConc_an,subclusterConc_in)                                             0.57
## cor(Intercept,subclusterEM)                                                         -0.49
## cor(subclusterConc_an,subclusterEM)                                                 -0.56
## cor(subclusterConc_in,subclusterEM)                                                 -0.57
## cor(Intercept,subclusterPS)                                                         -0.39
## cor(subclusterConc_an,subclusterPS)                                                 -0.64
## cor(subclusterConc_in,subclusterPS)                                                 -0.63
## cor(subclusterEM,subclusterPS)                                                      -0.47
## cor(Intercept,subclusterSS)                                                         -0.47
## cor(subclusterConc_an,subclusterSS)                                                 -0.53
## cor(subclusterConc_in,subclusterSS)                                                 -0.51
## cor(subclusterEM,subclusterSS)                                                      -0.52
## cor(subclusterPS,subclusterSS)                                                      -0.50
## cor(Intercept,self_contribution_c)                                                  -0.13
## cor(subclusterConc_an,self_contribution_c)                                          -0.49
## cor(subclusterConc_in,self_contribution_c)                                          -0.51
## cor(subclusterEM,self_contribution_c)                                               -0.52
## cor(subclusterPS,self_contribution_c)                                               -0.27
## cor(subclusterSS,self_contribution_c)                                               -0.47
## cor(Intercept,subclusterConc_an:self_contribution_c)                                -0.39
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                        -0.45
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                        -0.47
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                             -0.53
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                             -0.49
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                             -0.52
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                      -0.39
## cor(Intercept,subclusterConc_in:self_contribution_c)                                -0.42
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                        -0.41
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                        -0.37
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                             -0.58
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                             -0.45
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                             -0.53
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                      -0.52
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)    -0.45
## cor(Intercept,subclusterEM:self_contribution_c)                                     -0.44
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                             -0.49
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                             -0.49
## cor(subclusterEM,subclusterEM:self_contribution_c)                                  -0.48
## cor(subclusterPS,subclusterEM:self_contribution_c)                                  -0.62
## cor(subclusterSS,subclusterEM:self_contribution_c)                                  -0.53
## cor(self_contribution_c,subclusterEM:self_contribution_c)                           -0.70
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)         -0.53
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)         -0.59
## cor(Intercept,subclusterPS:self_contribution_c)                                     -0.48
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                             -0.52
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                             -0.50
## cor(subclusterEM,subclusterPS:self_contribution_c)                                  -0.56
## cor(subclusterPS,subclusterPS:self_contribution_c)                                  -0.49
## cor(subclusterSS,subclusterPS:self_contribution_c)                                  -0.53
## cor(self_contribution_c,subclusterPS:self_contribution_c)                           -0.51
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)         -0.53
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)         -0.51
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)              -0.51
## cor(Intercept,subclusterSS:self_contribution_c)                                     -0.44
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                             -0.55
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                             -0.59
## cor(subclusterEM,subclusterSS:self_contribution_c)                                  -0.51
## cor(subclusterPS,subclusterSS:self_contribution_c)                                  -0.52
## cor(subclusterSS,subclusterSS:self_contribution_c)                                  -0.55
## cor(self_contribution_c,subclusterSS:self_contribution_c)                           -0.52
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)         -0.53
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)         -0.56
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)              -0.50
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)              -0.51
##                                                                                  u-95% CI
## sd(Intercept)                                                                        3.46
## sd(subclusterConc_an)                                                                2.30
## sd(subclusterConc_in)                                                                2.54
## sd(subclusterEM)                                                                     1.21
## sd(subclusterPS)                                                                     1.93
## sd(subclusterSS)                                                                     1.35
## sd(self_contribution_c)                                                              0.08
## sd(subclusterConc_an:self_contribution_c)                                            0.08
## sd(subclusterConc_in:self_contribution_c)                                            0.07
## sd(subclusterEM:self_contribution_c)                                                 0.08
## sd(subclusterPS:self_contribution_c)                                                 0.08
## sd(subclusterSS:self_contribution_c)                                                 0.10
## cor(Intercept,subclusterConc_an)                                                     0.10
## cor(Intercept,subclusterConc_in)                                                     0.10
## cor(subclusterConc_an,subclusterConc_in)                                             0.92
## cor(Intercept,subclusterEM)                                                          0.49
## cor(subclusterConc_an,subclusterEM)                                                  0.47
## cor(subclusterConc_in,subclusterEM)                                                  0.45
## cor(Intercept,subclusterPS)                                                          0.42
## cor(subclusterConc_an,subclusterPS)                                                  0.24
## cor(subclusterConc_in,subclusterPS)                                                  0.21
## cor(subclusterEM,subclusterPS)                                                       0.57
## cor(Intercept,subclusterSS)                                                          0.52
## cor(subclusterConc_an,subclusterSS)                                                  0.49
## cor(subclusterConc_in,subclusterSS)                                                  0.51
## cor(subclusterEM,subclusterSS)                                                       0.55
## cor(subclusterPS,subclusterSS)                                                       0.57
## cor(Intercept,self_contribution_c)                                                   0.49
## cor(subclusterConc_an,self_contribution_c)                                           0.25
## cor(subclusterConc_in,self_contribution_c)                                           0.19
## cor(subclusterEM,self_contribution_c)                                                0.50
## cor(subclusterPS,self_contribution_c)                                                0.65
## cor(subclusterSS,self_contribution_c)                                                0.58
## cor(Intercept,subclusterConc_an:self_contribution_c)                                 0.55
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                         0.50
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                         0.48
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                              0.54
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                              0.54
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                              0.55
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                       0.63
## cor(Intercept,subclusterConc_in:self_contribution_c)                                 0.51
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                         0.55
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                         0.58
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                              0.49
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                              0.58
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                              0.55
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                       0.49
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)     0.68
## cor(Intercept,subclusterEM:self_contribution_c)                                      0.49
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                              0.47
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                              0.44
## cor(subclusterEM,subclusterEM:self_contribution_c)                                   0.56
## cor(subclusterPS,subclusterEM:self_contribution_c)                                   0.42
## cor(subclusterSS,subclusterEM:self_contribution_c)                                   0.54
## cor(self_contribution_c,subclusterEM:self_contribution_c)                            0.35
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)          0.51
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)          0.46
## cor(Intercept,subclusterPS:self_contribution_c)                                      0.50
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                              0.48
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                              0.51
## cor(subclusterEM,subclusterPS:self_contribution_c)                                   0.51
## cor(subclusterPS,subclusterPS:self_contribution_c)                                   0.56
## cor(subclusterSS,subclusterPS:self_contribution_c)                                   0.53
## cor(self_contribution_c,subclusterPS:self_contribution_c)                            0.54
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)          0.51
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)          0.56
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)               0.53
## cor(Intercept,subclusterSS:self_contribution_c)                                      0.48
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                              0.42
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                              0.38
## cor(subclusterEM,subclusterSS:self_contribution_c)                                   0.55
## cor(subclusterPS,subclusterSS:self_contribution_c)                                   0.53
## cor(subclusterSS,subclusterSS:self_contribution_c)                                   0.51
## cor(self_contribution_c,subclusterSS:self_contribution_c)                            0.51
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)          0.53
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)          0.49
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)               0.54
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)               0.54
##                                                                                  Rhat
## sd(Intercept)                                                                    1.00
## sd(subclusterConc_an)                                                            1.00
## sd(subclusterConc_in)                                                            1.00
## sd(subclusterEM)                                                                 1.00
## sd(subclusterPS)                                                                 1.00
## sd(subclusterSS)                                                                 1.00
## sd(self_contribution_c)                                                          1.00
## sd(subclusterConc_an:self_contribution_c)                                        1.00
## sd(subclusterConc_in:self_contribution_c)                                        1.00
## sd(subclusterEM:self_contribution_c)                                             1.00
## sd(subclusterPS:self_contribution_c)                                             1.00
## sd(subclusterSS:self_contribution_c)                                             1.00
## cor(Intercept,subclusterConc_an)                                                 1.00
## cor(Intercept,subclusterConc_in)                                                 1.00
## cor(subclusterConc_an,subclusterConc_in)                                         1.00
## cor(Intercept,subclusterEM)                                                      1.00
## cor(subclusterConc_an,subclusterEM)                                              1.00
## cor(subclusterConc_in,subclusterEM)                                              1.00
## cor(Intercept,subclusterPS)                                                      1.00
## cor(subclusterConc_an,subclusterPS)                                              1.00
## cor(subclusterConc_in,subclusterPS)                                              1.00
## cor(subclusterEM,subclusterPS)                                                   1.00
## cor(Intercept,subclusterSS)                                                      1.00
## cor(subclusterConc_an,subclusterSS)                                              1.00
## cor(subclusterConc_in,subclusterSS)                                              1.00
## cor(subclusterEM,subclusterSS)                                                   1.00
## cor(subclusterPS,subclusterSS)                                                   1.00
## cor(Intercept,self_contribution_c)                                               1.00
## cor(subclusterConc_an,self_contribution_c)                                       1.00
## cor(subclusterConc_in,self_contribution_c)                                       1.00
## cor(subclusterEM,self_contribution_c)                                            1.00
## cor(subclusterPS,self_contribution_c)                                            1.00
## cor(subclusterSS,self_contribution_c)                                            1.00
## cor(Intercept,subclusterConc_an:self_contribution_c)                             1.00
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                     1.00
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                     1.00
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                          1.00
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                          1.00
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                          1.00
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                   1.00
## cor(Intercept,subclusterConc_in:self_contribution_c)                             1.00
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                     1.00
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                     1.00
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                          1.00
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                          1.00
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                          1.00
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                   1.00
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 1.00
## cor(Intercept,subclusterEM:self_contribution_c)                                  1.00
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                          1.00
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                          1.00
## cor(subclusterEM,subclusterEM:self_contribution_c)                               1.00
## cor(subclusterPS,subclusterEM:self_contribution_c)                               1.00
## cor(subclusterSS,subclusterEM:self_contribution_c)                               1.00
## cor(self_contribution_c,subclusterEM:self_contribution_c)                        1.00
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)      1.00
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)      1.00
## cor(Intercept,subclusterPS:self_contribution_c)                                  1.00
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                          1.00
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                          1.00
## cor(subclusterEM,subclusterPS:self_contribution_c)                               1.00
## cor(subclusterPS,subclusterPS:self_contribution_c)                               1.00
## cor(subclusterSS,subclusterPS:self_contribution_c)                               1.00
## cor(self_contribution_c,subclusterPS:self_contribution_c)                        1.00
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)      1.00
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)      1.00
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)           1.00
## cor(Intercept,subclusterSS:self_contribution_c)                                  1.00
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                          1.00
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                          1.00
## cor(subclusterEM,subclusterSS:self_contribution_c)                               1.00
## cor(subclusterPS,subclusterSS:self_contribution_c)                               1.00
## cor(subclusterSS,subclusterSS:self_contribution_c)                               1.00
## cor(self_contribution_c,subclusterSS:self_contribution_c)                        1.00
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)      1.00
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)      1.00
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)           1.00
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)           1.00
##                                                                                  Bulk_ESS
## sd(Intercept)                                                                        2759
## sd(subclusterConc_an)                                                                2095
## sd(subclusterConc_in)                                                                2172
## sd(subclusterEM)                                                                     1945
## sd(subclusterPS)                                                                     1357
## sd(subclusterSS)                                                                     2636
## sd(self_contribution_c)                                                              1831
## sd(subclusterConc_an:self_contribution_c)                                            1698
## sd(subclusterConc_in:self_contribution_c)                                            1707
## sd(subclusterEM:self_contribution_c)                                                 2210
## sd(subclusterPS:self_contribution_c)                                                 2076
## sd(subclusterSS:self_contribution_c)                                                 2131
## cor(Intercept,subclusterConc_an)                                                     5361
## cor(Intercept,subclusterConc_in)                                                     5518
## cor(subclusterConc_an,subclusterConc_in)                                             3293
## cor(Intercept,subclusterEM)                                                         14840
## cor(subclusterConc_an,subclusterEM)                                                  9193
## cor(subclusterConc_in,subclusterEM)                                                  9183
## cor(Intercept,subclusterPS)                                                         10298
## cor(subclusterConc_an,subclusterPS)                                                  4968
## cor(subclusterConc_in,subclusterPS)                                                  6614
## cor(subclusterEM,subclusterPS)                                                       3689
## cor(Intercept,subclusterSS)                                                         14361
## cor(subclusterConc_an,subclusterSS)                                                 10547
## cor(subclusterConc_in,subclusterSS)                                                 11658
## cor(subclusterEM,subclusterSS)                                                       9059
## cor(subclusterPS,subclusterSS)                                                       9250
## cor(Intercept,self_contribution_c)                                                   5666
## cor(subclusterConc_an,self_contribution_c)                                           2656
## cor(subclusterConc_in,self_contribution_c)                                           3467
## cor(subclusterEM,self_contribution_c)                                                1457
## cor(subclusterPS,self_contribution_c)                                                1809
## cor(subclusterSS,self_contribution_c)                                                2088
## cor(Intercept,subclusterConc_an:self_contribution_c)                                 9655
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                         8913
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                         9449
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                              4799
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                              6049
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                              5761
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                       7016
## cor(Intercept,subclusterConc_in:self_contribution_c)                                10215
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                         8531
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                        10823
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                              5675
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                              5120
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                              7649
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                       7428
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)     3016
## cor(Intercept,subclusterEM:self_contribution_c)                                     11341
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                              9133
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                              9144
## cor(subclusterEM,subclusterEM:self_contribution_c)                                   5367
## cor(subclusterPS,subclusterEM:self_contribution_c)                                   5031
## cor(subclusterSS,subclusterEM:self_contribution_c)                                   6484
## cor(self_contribution_c,subclusterEM:self_contribution_c)                            5012
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)          6919
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)          6273
## cor(Intercept,subclusterPS:self_contribution_c)                                     12012
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                             10507
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                             11883
## cor(subclusterEM,subclusterPS:self_contribution_c)                                   7854
## cor(subclusterPS,subclusterPS:self_contribution_c)                                   9777
## cor(subclusterSS,subclusterPS:self_contribution_c)                                   8595
## cor(self_contribution_c,subclusterPS:self_contribution_c)                           10564
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)          8976
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)          8450
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)               8628
## cor(Intercept,subclusterSS:self_contribution_c)                                     11567
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                              9050
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                              9150
## cor(subclusterEM,subclusterSS:self_contribution_c)                                   6721
## cor(subclusterPS,subclusterSS:self_contribution_c)                                   8301
## cor(subclusterSS,subclusterSS:self_contribution_c)                                   6826
## cor(self_contribution_c,subclusterSS:self_contribution_c)                            7858
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)          7509
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)          7379
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)               8064
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)               7988
##                                                                                  Tail_ESS
## sd(Intercept)                                                                        5587
## sd(subclusterConc_an)                                                                3012
## sd(subclusterConc_in)                                                                3793
## sd(subclusterEM)                                                                     3478
## sd(subclusterPS)                                                                     2489
## sd(subclusterSS)                                                                     4349
## sd(self_contribution_c)                                                              2502
## sd(subclusterConc_an:self_contribution_c)                                            3790
## sd(subclusterConc_in:self_contribution_c)                                            3358
## sd(subclusterEM:self_contribution_c)                                                 4456
## sd(subclusterPS:self_contribution_c)                                                 4062
## sd(subclusterSS:self_contribution_c)                                                 4128
## cor(Intercept,subclusterConc_an)                                                     6777
## cor(Intercept,subclusterConc_in)                                                     7496
## cor(subclusterConc_an,subclusterConc_in)                                             5743
## cor(Intercept,subclusterEM)                                                          9087
## cor(subclusterConc_an,subclusterEM)                                                  8656
## cor(subclusterConc_in,subclusterEM)                                                  8642
## cor(Intercept,subclusterPS)                                                          8655
## cor(subclusterConc_an,subclusterPS)                                                  7128
## cor(subclusterConc_in,subclusterPS)                                                  7720
## cor(subclusterEM,subclusterPS)                                                       6998
## cor(Intercept,subclusterSS)                                                          8252
## cor(subclusterConc_an,subclusterSS)                                                  8668
## cor(subclusterConc_in,subclusterSS)                                                  9608
## cor(subclusterEM,subclusterSS)                                                      10055
## cor(subclusterPS,subclusterSS)                                                       8737
## cor(Intercept,self_contribution_c)                                                   8162
## cor(subclusterConc_an,self_contribution_c)                                           4717
## cor(subclusterConc_in,self_contribution_c)                                           6288
## cor(subclusterEM,self_contribution_c)                                                3596
## cor(subclusterPS,self_contribution_c)                                                3448
## cor(subclusterSS,self_contribution_c)                                                4276
## cor(Intercept,subclusterConc_an:self_contribution_c)                                 8264
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                         8652
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                         9308
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                              8520
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                              8897
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                              8443
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                       7868
## cor(Intercept,subclusterConc_in:self_contribution_c)                                 7451
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                         9204
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                         8284
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                              7924
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                              9051
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                              9160
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                       9257
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)     6450
## cor(Intercept,subclusterEM:self_contribution_c)                                      7977
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                              8335
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                              9217
## cor(subclusterEM,subclusterEM:self_contribution_c)                                   7501
## cor(subclusterPS,subclusterEM:self_contribution_c)                                   8041
## cor(subclusterSS,subclusterEM:self_contribution_c)                                   8845
## cor(self_contribution_c,subclusterEM:self_contribution_c)                            8257
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)          9112
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)          9469
## cor(Intercept,subclusterPS:self_contribution_c)                                      8645
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                              9035
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                              9062
## cor(subclusterEM,subclusterPS:self_contribution_c)                                   9328
## cor(subclusterPS,subclusterPS:self_contribution_c)                                   9630
## cor(subclusterSS,subclusterPS:self_contribution_c)                                   9044
## cor(self_contribution_c,subclusterPS:self_contribution_c)                            9875
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)          9975
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)          9708
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)              10203
## cor(Intercept,subclusterSS:self_contribution_c)                                      7924
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                              7797
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                              7576
## cor(subclusterEM,subclusterSS:self_contribution_c)                                   9121
## cor(subclusterPS,subclusterSS:self_contribution_c)                                   9340
## cor(subclusterSS,subclusterSS:self_contribution_c)                                   8861
## cor(self_contribution_c,subclusterSS:self_contribution_c)                            8064
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)          9548
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)         10200
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)              10121
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)               9628
## 
## ~word (Number of levels: 32) 
##                                    Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                          0.14      0.10     0.01     0.36 1.00
## sd(self_contribution_c)                0.01      0.01     0.00     0.02 1.00
## cor(Intercept,self_contribution_c)     0.19      0.55    -0.90     0.97 1.00
##                                    Bulk_ESS Tail_ESS
## sd(Intercept)                          3960     4438
## sd(self_contribution_c)                3030     4923
## cor(Intercept,self_contribution_c)     4787     7580
## 
## Population-Level Effects: 
##                                       Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1]                             -5.96      0.44    -6.84    -5.09 1.00
## Intercept[2]                             -2.03      0.35    -2.73    -1.35 1.00
## Intercept[3]                              0.89      0.35     0.23     1.57 1.00
## Intercept[4]                              3.33      0.37     2.59     4.07 1.00
## Intercept[5]                              6.16      0.46     5.29     7.09 1.00
## subclusterConc_an                        -0.13      0.30    -0.72     0.45 1.00
## subclusterConc_in                         0.00      0.31    -0.61     0.62 1.00
## subclusterEM                              0.12      0.28    -0.43     0.67 1.00
## subclusterPS                             -0.15      0.31    -0.78     0.44 1.00
## subclusterSS                             -0.27      0.33    -0.93     0.36 1.00
## self_contribution_c                       0.06      0.02     0.04     0.09 1.00
## difficulty_c                             -0.04      0.00    -0.04    -0.03 1.00
## subclusterConc_an:self_contribution_c    -0.02      0.02    -0.05     0.01 1.00
## subclusterConc_in:self_contribution_c    -0.00      0.02    -0.04     0.03 1.00
## subclusterEM:self_contribution_c          0.00      0.02    -0.03     0.03 1.00
## subclusterPS:self_contribution_c         -0.02      0.02    -0.05     0.02 1.00
## subclusterSS:self_contribution_c         -0.01      0.02    -0.05     0.03 1.00
##                                       Bulk_ESS Tail_ESS
## Intercept[1]                              2707     5030
## Intercept[2]                              2654     4460
## Intercept[3]                              2555     4743
## Intercept[4]                              2423     4220
## Intercept[5]                              2649     5530
## subclusterConc_an                         5624     7214
## subclusterConc_in                         5581     6793
## subclusterEM                              6802     8157
## subclusterPS                              6577     7619
## subclusterSS                              7124     8546
## self_contribution_c                       4271     6278
## difficulty_c                              7499     8787
## subclusterConc_an:self_contribution_c     5212     6643
## subclusterConc_in:self_contribution_c     5008     7344
## subclusterEM:self_contribution_c          5883     7399
## subclusterPS:self_contribution_c          6065     7495
## subclusterSS:self_contribution_c          6671     7369
## 
## Family Specific Parameters: 
##      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc     1.00      0.00     1.00     1.00   NA       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(subcluster_self_mdl,
           'self_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0     0.06      0.02     0.04     0.09        Inf
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_self_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.04         0    -0.04    -0.03        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_self_mdl,
           'subclusterConc_an:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_a... < 0    -0.02      0.02    -0.05     0.01       7.22
##   Post.Prob Star
## 1      0.88     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_self_mdl,
           'subclusterConc_in:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_i... < 0        0      0.02    -0.03     0.03       1.33
##   Post.Prob Star
## 1      0.57     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_self_mdl,
           'subclusterEM:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:sel... < 0        0      0.02    -0.03     0.03       0.94
##   Post.Prob Star
## 1      0.48     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_self_mdl,
           'subclusterPS:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:sel... < 0    -0.02      0.02    -0.04     0.01       4.18
##   Post.Prob Star
## 1      0.81     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_self_mdl,
           'subclusterSS:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:sel... < 0    -0.01      0.02    -0.04     0.03       1.77
##   Post.Prob Star
## 1      0.64     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Re-do the self main model, the one with closeness_01 as dependent variable, this time also with a difficulty_c control covariate:

subcluster_dist_self_mdl <- brm(bf(closeness_01 ~ 
                                      
                             # Fixed effects:
                                      
                             1 +
                             subcluster +
                             self_contribution_c +
                             difficulty_c +
                             subcluster:self_contribution_c +
                                      
                             # Random effects:
                                      
                             (1 +
                                subcluster +
                                self_contribution_c +
                                         subcluster:self_contribution_c|participant) +
                             (1 + self_contribution_c|word),
                             phi ~ 1 + subcluster),
           
                           data = df,
                           family = Beta,
           
                           # MCMC settings:
           
                           seed = 42,
                           init = 0,
                           cores = 4,
                           iter = 6000,
                           warmup = 3000,
                           control = list(adapt_delta = 0.99))

# Save model:

save(subcluster_dist_self_mdl,
     file = '../models_E2/subcluster_dist_self_mdl.RData')

Load model:

load('../models_E2/subcluster_dist_self_mdl.Rdata')

Show priors:

prior_summary(subcluster_dist_self_mdl)
##                 prior     class                                  coef
##                (flat)         b                                      
##                (flat)         b                          difficulty_c
##                (flat)         b                   self_contribution_c
##                (flat)         b                     subclusterConc_an
##                (flat)         b subclusterConc_an:self_contribution_c
##                (flat)         b                     subclusterConc_in
##                (flat)         b subclusterConc_in:self_contribution_c
##                (flat)         b                          subclusterEM
##                (flat)         b      subclusterEM:self_contribution_c
##                (flat)         b                          subclusterPS
##                (flat)         b      subclusterPS:self_contribution_c
##                (flat)         b                          subclusterSS
##                (flat)         b      subclusterSS:self_contribution_c
##                (flat)         b                                      
##                (flat)         b                     subclusterConc_an
##                (flat)         b                     subclusterConc_in
##                (flat)         b                          subclusterEM
##                (flat)         b                          subclusterPS
##                (flat)         b                          subclusterSS
##  student_t(3, 0, 2.5) Intercept                                      
##  student_t(3, 0, 2.5) Intercept                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  lkj_corr_cholesky(1)         L                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                   self_contribution_c
##  student_t(3, 0, 2.5)        sd                     subclusterConc_an
##  student_t(3, 0, 2.5)        sd subclusterConc_an:self_contribution_c
##  student_t(3, 0, 2.5)        sd                     subclusterConc_in
##  student_t(3, 0, 2.5)        sd subclusterConc_in:self_contribution_c
##  student_t(3, 0, 2.5)        sd                          subclusterEM
##  student_t(3, 0, 2.5)        sd      subclusterEM:self_contribution_c
##  student_t(3, 0, 2.5)        sd                          subclusterPS
##  student_t(3, 0, 2.5)        sd      subclusterPS:self_contribution_c
##  student_t(3, 0, 2.5)        sd                          subclusterSS
##  student_t(3, 0, 2.5)        sd      subclusterSS:self_contribution_c
##  student_t(3, 0, 2.5)        sd                                      
##  student_t(3, 0, 2.5)        sd                             Intercept
##  student_t(3, 0, 2.5)        sd                   self_contribution_c
##        group resp dpar nlpar lb ub       source
##                                         default
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                                    (vectorized)
##                    phi                  default
##                    phi             (vectorized)
##                    phi             (vectorized)
##                    phi             (vectorized)
##                    phi             (vectorized)
##                    phi             (vectorized)
##                                         default
##                    phi                  default
##                                         default
##  participant                       (vectorized)
##         word                       (vectorized)
##                               0         default
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##  participant                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)
##         word                  0    (vectorized)

Check posterior predictive checks of the mixed beta regression:

pp_check(subcluster_dist_self_mdl, ndraws = 100)

Check this model:

subcluster_dist_self_mdl
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Warning: There were 252 divergent transitions after warmup. Increasing
## adapt_delta above 0.99 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: closeness_01 ~ 1 + subcluster + self_contribution_c + difficulty_c + subcluster:self_contribution_c + (1 + subcluster + self_contribution_c + subcluster:self_contribution_c | participant) + (1 + self_contribution_c | word) 
##          phi ~ 1 + subcluster
##    Data: df (Number of observations: 1032) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                                  Estimate
## sd(Intercept)                                                                        0.84
## sd(subclusterConc_an)                                                                0.62
## sd(subclusterConc_in)                                                                0.49
## sd(subclusterEM)                                                                     0.37
## sd(subclusterPS)                                                                     0.61
## sd(subclusterSS)                                                                     0.32
## sd(self_contribution_c)                                                              0.02
## sd(subclusterConc_an:self_contribution_c)                                            0.01
## sd(subclusterConc_in:self_contribution_c)                                            0.00
## sd(subclusterEM:self_contribution_c)                                                 0.01
## sd(subclusterPS:self_contribution_c)                                                 0.02
## sd(subclusterSS:self_contribution_c)                                                 0.01
## cor(Intercept,subclusterConc_an)                                                    -0.19
## cor(Intercept,subclusterConc_in)                                                    -0.16
## cor(subclusterConc_an,subclusterConc_in)                                             0.88
## cor(Intercept,subclusterEM)                                                         -0.03
## cor(subclusterConc_an,subclusterEM)                                                  0.18
## cor(subclusterConc_in,subclusterEM)                                                  0.12
## cor(Intercept,subclusterPS)                                                          0.05
## cor(subclusterConc_an,subclusterPS)                                                  0.08
## cor(subclusterConc_in,subclusterPS)                                                  0.03
## cor(subclusterEM,subclusterPS)                                                       0.27
## cor(Intercept,subclusterSS)                                                          0.19
## cor(subclusterConc_an,subclusterSS)                                                 -0.02
## cor(subclusterConc_in,subclusterSS)                                                 -0.12
## cor(subclusterEM,subclusterSS)                                                       0.10
## cor(subclusterPS,subclusterSS)                                                       0.38
## cor(Intercept,self_contribution_c)                                                   0.04
## cor(subclusterConc_an,self_contribution_c)                                           0.08
## cor(subclusterConc_in,self_contribution_c)                                           0.11
## cor(subclusterEM,self_contribution_c)                                                0.07
## cor(subclusterPS,self_contribution_c)                                                0.03
## cor(subclusterSS,self_contribution_c)                                                0.24
## cor(Intercept,subclusterConc_an:self_contribution_c)                                 0.14
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                        -0.06
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                        -0.04
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                             -0.01
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                             -0.12
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                             -0.03
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                       0.03
## cor(Intercept,subclusterConc_in:self_contribution_c)                                -0.05
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                         0.12
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                         0.12
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                             -0.15
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                             -0.07
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                              0.04
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                       0.08
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)     0.19
## cor(Intercept,subclusterEM:self_contribution_c)                                      0.11
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                              0.17
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                              0.16
## cor(subclusterEM,subclusterEM:self_contribution_c)                                   0.38
## cor(subclusterPS,subclusterEM:self_contribution_c)                                   0.01
## cor(subclusterSS,subclusterEM:self_contribution_c)                                   0.04
## cor(self_contribution_c,subclusterEM:self_contribution_c)                            0.21
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)          0.03
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)          0.06
## cor(Intercept,subclusterPS:self_contribution_c)                                      0.24
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                             -0.19
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                             -0.33
## cor(subclusterEM,subclusterPS:self_contribution_c)                                   0.01
## cor(subclusterPS,subclusterPS:self_contribution_c)                                   0.53
## cor(subclusterSS,subclusterPS:self_contribution_c)                                   0.44
## cor(self_contribution_c,subclusterPS:self_contribution_c)                           -0.16
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)         -0.06
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)         -0.12
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)              -0.06
## cor(Intercept,subclusterSS:self_contribution_c)                                     -0.15
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                              0.31
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                              0.30
## cor(subclusterEM,subclusterSS:self_contribution_c)                                   0.06
## cor(subclusterPS,subclusterSS:self_contribution_c)                                   0.25
## cor(subclusterSS,subclusterSS:self_contribution_c)                                   0.21
## cor(self_contribution_c,subclusterSS:self_contribution_c)                            0.20
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)         -0.04
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)          0.08
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)               0.10
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)               0.11
##                                                                                  Est.Error
## sd(Intercept)                                                                         0.10
## sd(subclusterConc_an)                                                                 0.08
## sd(subclusterConc_in)                                                                 0.06
## sd(subclusterEM)                                                                      0.06
## sd(subclusterPS)                                                                      0.09
## sd(subclusterSS)                                                                      0.07
## sd(self_contribution_c)                                                               0.00
## sd(subclusterConc_an:self_contribution_c)                                             0.00
## sd(subclusterConc_in:self_contribution_c)                                             0.00
## sd(subclusterEM:self_contribution_c)                                                  0.00
## sd(subclusterPS:self_contribution_c)                                                  0.01
## sd(subclusterSS:self_contribution_c)                                                  0.00
## cor(Intercept,subclusterConc_an)                                                      0.14
## cor(Intercept,subclusterConc_in)                                                      0.13
## cor(subclusterConc_an,subclusterConc_in)                                              0.04
## cor(Intercept,subclusterEM)                                                           0.14
## cor(subclusterConc_an,subclusterEM)                                                   0.15
## cor(subclusterConc_in,subclusterEM)                                                   0.16
## cor(Intercept,subclusterPS)                                                           0.11
## cor(subclusterConc_an,subclusterPS)                                                   0.14
## cor(subclusterConc_in,subclusterPS)                                                   0.20
## cor(subclusterEM,subclusterPS)                                                        0.23
## cor(Intercept,subclusterSS)                                                           0.16
## cor(subclusterConc_an,subclusterSS)                                                   0.26
## cor(subclusterConc_in,subclusterSS)                                                   0.25
## cor(subclusterEM,subclusterSS)                                                        0.22
## cor(subclusterPS,subclusterSS)                                                        0.25
## cor(Intercept,self_contribution_c)                                                    0.11
## cor(subclusterConc_an,self_contribution_c)                                            0.16
## cor(subclusterConc_in,self_contribution_c)                                            0.16
## cor(subclusterEM,self_contribution_c)                                                 0.16
## cor(subclusterPS,self_contribution_c)                                                 0.13
## cor(subclusterSS,self_contribution_c)                                                 0.24
## cor(Intercept,subclusterConc_an:self_contribution_c)                                  0.24
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                          0.21
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                          0.23
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                               0.22
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                               0.24
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                               0.25
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                        0.25
## cor(Intercept,subclusterConc_in:self_contribution_c)                                  0.22
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                          0.25
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                          0.23
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                               0.26
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                               0.25
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                               0.24
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                        0.25
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)      0.28
## cor(Intercept,subclusterEM:self_contribution_c)                                       0.21
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                               0.27
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                               0.29
## cor(subclusterEM,subclusterEM:self_contribution_c)                                    0.21
## cor(subclusterPS,subclusterEM:self_contribution_c)                                    0.24
## cor(subclusterSS,subclusterEM:self_contribution_c)                                    0.26
## cor(self_contribution_c,subclusterEM:self_contribution_c)                             0.32
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)           0.23
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)           0.28
## cor(Intercept,subclusterPS:self_contribution_c)                                       0.14
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                               0.15
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                               0.15
## cor(subclusterEM,subclusterPS:self_contribution_c)                                    0.21
## cor(subclusterPS,subclusterPS:self_contribution_c)                                    0.15
## cor(subclusterSS,subclusterPS:self_contribution_c)                                    0.25
## cor(self_contribution_c,subclusterPS:self_contribution_c)                             0.17
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)           0.26
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)           0.23
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)                0.24
## cor(Intercept,subclusterSS:self_contribution_c)                                       0.22
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                               0.18
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                               0.18
## cor(subclusterEM,subclusterSS:self_contribution_c)                                    0.23
## cor(subclusterPS,subclusterSS:self_contribution_c)                                    0.22
## cor(subclusterSS,subclusterSS:self_contribution_c)                                    0.25
## cor(self_contribution_c,subclusterSS:self_contribution_c)                             0.19
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)           0.23
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)           0.33
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)                0.24
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)                0.23
##                                                                                  l-95% CI
## sd(Intercept)                                                                        0.67
## sd(subclusterConc_an)                                                                0.48
## sd(subclusterConc_in)                                                                0.37
## sd(subclusterEM)                                                                     0.25
## sd(subclusterPS)                                                                     0.43
## sd(subclusterSS)                                                                     0.12
## sd(self_contribution_c)                                                              0.01
## sd(subclusterConc_an:self_contribution_c)                                            0.00
## sd(subclusterConc_in:self_contribution_c)                                            0.00
## sd(subclusterEM:self_contribution_c)                                                 0.00
## sd(subclusterPS:self_contribution_c)                                                 0.01
## sd(subclusterSS:self_contribution_c)                                                 0.00
## cor(Intercept,subclusterConc_an)                                                    -0.38
## cor(Intercept,subclusterConc_in)                                                    -0.36
## cor(subclusterConc_an,subclusterConc_in)                                             0.78
## cor(Intercept,subclusterEM)                                                         -0.27
## cor(subclusterConc_an,subclusterEM)                                                 -0.17
## cor(subclusterConc_in,subclusterEM)                                                 -0.22
## cor(Intercept,subclusterPS)                                                         -0.17
## cor(subclusterConc_an,subclusterPS)                                                 -0.20
## cor(subclusterConc_in,subclusterPS)                                                 -0.30
## cor(subclusterEM,subclusterPS)                                                      -0.20
## cor(Intercept,subclusterSS)                                                         -0.09
## cor(subclusterConc_an,subclusterSS)                                                 -0.46
## cor(subclusterConc_in,subclusterSS)                                                 -0.53
## cor(subclusterEM,subclusterSS)                                                      -0.39
## cor(subclusterPS,subclusterSS)                                                      -0.16
## cor(Intercept,self_contribution_c)                                                  -0.18
## cor(subclusterConc_an,self_contribution_c)                                          -0.28
## cor(subclusterConc_in,self_contribution_c)                                          -0.25
## cor(subclusterEM,self_contribution_c)                                               -0.29
## cor(subclusterPS,self_contribution_c)                                               -0.26
## cor(subclusterSS,self_contribution_c)                                               -0.16
## cor(Intercept,subclusterConc_an:self_contribution_c)                                -0.42
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                        -0.49
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                        -0.55
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                             -0.44
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                             -0.56
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                             -0.56
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                      -0.51
## cor(Intercept,subclusterConc_in:self_contribution_c)                                -0.51
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                        -0.40
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                        -0.40
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                             -0.71
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                             -0.60
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                             -0.46
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                      -0.42
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)    -0.41
## cor(Intercept,subclusterEM:self_contribution_c)                                     -0.34
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                             -0.36
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                             -0.39
## cor(subclusterEM,subclusterEM:self_contribution_c)                                  -0.13
## cor(subclusterPS,subclusterEM:self_contribution_c)                                  -0.47
## cor(subclusterSS,subclusterEM:self_contribution_c)                                  -0.49
## cor(self_contribution_c,subclusterEM:self_contribution_c)                           -0.39
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)         -0.43
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)         -0.48
## cor(Intercept,subclusterPS:self_contribution_c)                                     -0.09
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                             -0.47
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                             -0.58
## cor(subclusterEM,subclusterPS:self_contribution_c)                                  -0.42
## cor(subclusterPS,subclusterPS:self_contribution_c)                                   0.17
## cor(subclusterSS,subclusterPS:self_contribution_c)                                  -0.15
## cor(self_contribution_c,subclusterPS:self_contribution_c)                           -0.51
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)         -0.53
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)         -0.57
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)              -0.47
## cor(Intercept,subclusterSS:self_contribution_c)                                     -0.45
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                             -0.10
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                             -0.11
## cor(subclusterEM,subclusterSS:self_contribution_c)                                  -0.41
## cor(subclusterPS,subclusterSS:self_contribution_c)                                  -0.27
## cor(subclusterSS,subclusterSS:self_contribution_c)                                  -0.34
## cor(self_contribution_c,subclusterSS:self_contribution_c)                           -0.24
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)         -0.49
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)         -0.52
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)              -0.40
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)              -0.38
##                                                                                  u-95% CI
## sd(Intercept)                                                                        0.98
## sd(subclusterConc_an)                                                                0.73
## sd(subclusterConc_in)                                                                0.60
## sd(subclusterEM)                                                                     0.52
## sd(subclusterPS)                                                                     0.80
## sd(subclusterSS)                                                                     0.44
## sd(self_contribution_c)                                                              0.02
## sd(subclusterConc_an:self_contribution_c)                                            0.02
## sd(subclusterConc_in:self_contribution_c)                                            0.01
## sd(subclusterEM:self_contribution_c)                                                 0.02
## sd(subclusterPS:self_contribution_c)                                                 0.04
## sd(subclusterSS:self_contribution_c)                                                 0.02
## cor(Intercept,subclusterConc_an)                                                     0.08
## cor(Intercept,subclusterConc_in)                                                     0.10
## cor(subclusterConc_an,subclusterConc_in)                                             0.95
## cor(Intercept,subclusterEM)                                                          0.29
## cor(subclusterConc_an,subclusterEM)                                                  0.41
## cor(subclusterConc_in,subclusterEM)                                                  0.39
## cor(Intercept,subclusterPS)                                                          0.31
## cor(subclusterConc_an,subclusterPS)                                                  0.32
## cor(subclusterConc_in,subclusterPS)                                                  0.30
## cor(subclusterEM,subclusterPS)                                                       0.59
## cor(Intercept,subclusterSS)                                                          0.55
## cor(subclusterConc_an,subclusterSS)                                                  0.33
## cor(subclusterConc_in,subclusterSS)                                                  0.22
## cor(subclusterEM,subclusterSS)                                                       0.40
## cor(subclusterPS,subclusterSS)                                                       0.67
## cor(Intercept,self_contribution_c)                                                   0.29
## cor(subclusterConc_an,self_contribution_c)                                           0.36
## cor(subclusterConc_in,self_contribution_c)                                           0.39
## cor(subclusterEM,self_contribution_c)                                                0.40
## cor(subclusterPS,self_contribution_c)                                                0.31
## cor(subclusterSS,self_contribution_c)                                                0.58
## cor(Intercept,subclusterConc_an:self_contribution_c)                                 0.48
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                         0.35
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                         0.42
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                              0.44
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                              0.45
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                              0.47
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                       0.44
## cor(Intercept,subclusterConc_in:self_contribution_c)                                 0.36
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                         0.46
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                         0.50
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                              0.37
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                              0.37
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                              0.43
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                       0.46
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)     0.64
## cor(Intercept,subclusterEM:self_contribution_c)                                      0.52
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                              0.54
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                              0.58
## cor(subclusterEM,subclusterEM:self_contribution_c)                                   0.74
## cor(subclusterPS,subclusterEM:self_contribution_c)                                   0.39
## cor(subclusterSS,subclusterEM:self_contribution_c)                                   0.46
## cor(self_contribution_c,subclusterEM:self_contribution_c)                            0.64
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)          0.53
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)          0.45
## cor(Intercept,subclusterPS:self_contribution_c)                                      0.51
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                              0.13
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                              0.03
## cor(subclusterEM,subclusterPS:self_contribution_c)                                   0.39
## cor(subclusterPS,subclusterPS:self_contribution_c)                                   0.77
## cor(subclusterSS,subclusterPS:self_contribution_c)                                   0.82
## cor(self_contribution_c,subclusterPS:self_contribution_c)                            0.21
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)          0.52
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)          0.35
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)               0.43
## cor(Intercept,subclusterSS:self_contribution_c)                                      0.31
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                              0.62
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                              0.62
## cor(subclusterEM,subclusterSS:self_contribution_c)                                   0.38
## cor(subclusterPS,subclusterSS:self_contribution_c)                                   0.57
## cor(subclusterSS,subclusterSS:self_contribution_c)                                   0.53
## cor(self_contribution_c,subclusterSS:self_contribution_c)                            0.54
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)          0.43
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)          0.51
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)               0.53
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)               0.56
##                                                                                  Rhat
## sd(Intercept)                                                                    1.76
## sd(subclusterConc_an)                                                            1.32
## sd(subclusterConc_in)                                                            1.23
## sd(subclusterEM)                                                                 1.26
## sd(subclusterPS)                                                                 1.24
## sd(subclusterSS)                                                                 1.46
## sd(self_contribution_c)                                                          1.21
## sd(subclusterConc_an:self_contribution_c)                                        1.18
## sd(subclusterConc_in:self_contribution_c)                                        1.34
## sd(subclusterEM:self_contribution_c)                                             1.42
## sd(subclusterPS:self_contribution_c)                                             1.57
## sd(subclusterSS:self_contribution_c)                                             1.37
## cor(Intercept,subclusterConc_an)                                                 1.43
## cor(Intercept,subclusterConc_in)                                                 1.20
## cor(subclusterConc_an,subclusterConc_in)                                         1.26
## cor(Intercept,subclusterEM)                                                      1.13
## cor(subclusterConc_an,subclusterEM)                                              1.17
## cor(subclusterConc_in,subclusterEM)                                              1.15
## cor(Intercept,subclusterPS)                                                      1.18
## cor(subclusterConc_an,subclusterPS)                                              1.27
## cor(subclusterConc_in,subclusterPS)                                              1.56
## cor(subclusterEM,subclusterPS)                                                   1.64
## cor(Intercept,subclusterSS)                                                      1.22
## cor(subclusterConc_an,subclusterSS)                                              1.58
## cor(subclusterConc_in,subclusterSS)                                              1.53
## cor(subclusterEM,subclusterSS)                                                   1.32
## cor(subclusterPS,subclusterSS)                                                   1.63
## cor(Intercept,self_contribution_c)                                               1.26
## cor(subclusterConc_an,self_contribution_c)                                       1.49
## cor(subclusterConc_in,self_contribution_c)                                       1.44
## cor(subclusterEM,self_contribution_c)                                            1.26
## cor(subclusterPS,self_contribution_c)                                            1.31
## cor(subclusterSS,self_contribution_c)                                            1.43
## cor(Intercept,subclusterConc_an:self_contribution_c)                             1.21
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                     1.28
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                     1.39
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                          1.38
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                          1.36
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                          1.22
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                   1.29
## cor(Intercept,subclusterConc_in:self_contribution_c)                             1.23
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                     1.21
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                     1.10
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                          1.49
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                          1.19
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                          1.20
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                   1.28
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 1.14
## cor(Intercept,subclusterEM:self_contribution_c)                                  1.18
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                          1.41
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                          1.49
## cor(subclusterEM,subclusterEM:self_contribution_c)                               1.28
## cor(subclusterPS,subclusterEM:self_contribution_c)                               1.24
## cor(subclusterSS,subclusterEM:self_contribution_c)                               1.20
## cor(self_contribution_c,subclusterEM:self_contribution_c)                        1.41
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)      1.25
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)      1.29
## cor(Intercept,subclusterPS:self_contribution_c)                                  1.19
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                          1.13
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                          1.11
## cor(subclusterEM,subclusterPS:self_contribution_c)                               1.29
## cor(subclusterPS,subclusterPS:self_contribution_c)                               1.19
## cor(subclusterSS,subclusterPS:self_contribution_c)                               1.60
## cor(self_contribution_c,subclusterPS:self_contribution_c)                        1.27
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)      1.42
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)      1.25
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)           1.20
## cor(Intercept,subclusterSS:self_contribution_c)                                  1.31
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                          1.11
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                          1.11
## cor(subclusterEM,subclusterSS:self_contribution_c)                               1.18
## cor(subclusterPS,subclusterSS:self_contribution_c)                               1.20
## cor(subclusterSS,subclusterSS:self_contribution_c)                               1.33
## cor(self_contribution_c,subclusterSS:self_contribution_c)                        1.22
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)      1.26
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)      1.52
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)           1.15
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)           1.18
##                                                                                  Bulk_ESS
## sd(Intercept)                                                                           6
## sd(subclusterConc_an)                                                                  10
## sd(subclusterConc_in)                                                                  13
## sd(subclusterEM)                                                                       38
## sd(subclusterPS)                                                                       14
## sd(subclusterSS)                                                                       81
## sd(self_contribution_c)                                                                14
## sd(subclusterConc_an:self_contribution_c)                                              70
## sd(subclusterConc_in:self_contribution_c)                                              48
## sd(subclusterEM:self_contribution_c)                                                    8
## sd(subclusterPS:self_contribution_c)                                                   11
## sd(subclusterSS:self_contribution_c)                                                   20
## cor(Intercept,subclusterConc_an)                                                        8
## cor(Intercept,subclusterConc_in)                                                       15
## cor(subclusterConc_an,subclusterConc_in)                                               20
## cor(Intercept,subclusterEM)                                                            24
## cor(subclusterConc_an,subclusterEM)                                                    18
## cor(subclusterConc_in,subclusterEM)                                                    22
## cor(Intercept,subclusterPS)                                                            39
## cor(subclusterConc_an,subclusterPS)                                                    12
## cor(subclusterConc_in,subclusterPS)                                                     7
## cor(subclusterEM,subclusterPS)                                                          7
## cor(Intercept,subclusterSS)                                                            35
## cor(subclusterConc_an,subclusterSS)                                                     7
## cor(subclusterConc_in,subclusterSS)                                                     7
## cor(subclusterEM,subclusterSS)                                                         10
## cor(subclusterPS,subclusterSS)                                                          7
## cor(Intercept,self_contribution_c)                                                     78
## cor(subclusterConc_an,self_contribution_c)                                             10
## cor(subclusterConc_in,self_contribution_c)                                             12
## cor(subclusterEM,self_contribution_c)                                                  28
## cor(subclusterPS,self_contribution_c)                                                  37
## cor(subclusterSS,self_contribution_c)                                                   9
## cor(Intercept,subclusterConc_an:self_contribution_c)                                   15
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                           22
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                           28
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                                64
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                                74
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                                66
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                         11
## cor(Intercept,subclusterConc_in:self_contribution_c)                                   62
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                           13
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                           28
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                                28
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                                16
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                                14
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                         11
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)       19
## cor(Intercept,subclusterEM:self_contribution_c)                                        18
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                                 8
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                                 8
## cor(subclusterEM,subclusterEM:self_contribution_c)                                     94
## cor(subclusterPS,subclusterEM:self_contribution_c)                                     12
## cor(subclusterSS,subclusterEM:self_contribution_c)                                     15
## cor(self_contribution_c,subclusterEM:self_contribution_c)                               9
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)           108
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)            11
## cor(Intercept,subclusterPS:self_contribution_c)                                        24
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                                22
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                                26
## cor(subclusterEM,subclusterPS:self_contribution_c)                                     11
## cor(subclusterPS,subclusterPS:self_contribution_c)                                     16
## cor(subclusterSS,subclusterPS:self_contribution_c)                                      7
## cor(self_contribution_c,subclusterPS:self_contribution_c)                             174
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)            55
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)            20
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)                 15
## cor(Intercept,subclusterSS:self_contribution_c)                                        10
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                                27
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                                27
## cor(subclusterEM,subclusterSS:self_contribution_c)                                     16
## cor(subclusterPS,subclusterSS:self_contribution_c)                                     14
## cor(subclusterSS,subclusterSS:self_contribution_c)                                     10
## cor(self_contribution_c,subclusterSS:self_contribution_c)                              67
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)            76
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)             7
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)                 20
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)                 16
##                                                                                  Tail_ESS
## sd(Intercept)                                                                          18
## sd(subclusterConc_an)                                                                 169
## sd(subclusterConc_in)                                                                 134
## sd(subclusterEM)                                                                      131
## sd(subclusterPS)                                                                       64
## sd(subclusterSS)                                                                       62
## sd(self_contribution_c)                                                               170
## sd(subclusterConc_an:self_contribution_c)                                              95
## sd(subclusterConc_in:self_contribution_c)                                             117
## sd(subclusterEM:self_contribution_c)                                                   24
## sd(subclusterPS:self_contribution_c)                                                   28
## sd(subclusterSS:self_contribution_c)                                                   49
## cor(Intercept,subclusterConc_an)                                                       44
## cor(Intercept,subclusterConc_in)                                                      123
## cor(subclusterConc_an,subclusterConc_in)                                               59
## cor(Intercept,subclusterEM)                                                           140
## cor(subclusterConc_an,subclusterEM)                                                   107
## cor(subclusterConc_in,subclusterEM)                                                    68
## cor(Intercept,subclusterPS)                                                           128
## cor(subclusterConc_an,subclusterPS)                                                   127
## cor(subclusterConc_in,subclusterPS)                                                    57
## cor(subclusterEM,subclusterPS)                                                         18
## cor(Intercept,subclusterSS)                                                            75
## cor(subclusterConc_an,subclusterSS)                                                    34
## cor(subclusterConc_in,subclusterSS)                                                   106
## cor(subclusterEM,subclusterSS)                                                         54
## cor(subclusterPS,subclusterSS)                                                         18
## cor(Intercept,self_contribution_c)                                                    180
## cor(subclusterConc_an,self_contribution_c)                                             26
## cor(subclusterConc_in,self_contribution_c)                                             36
## cor(subclusterEM,self_contribution_c)                                                  86
## cor(subclusterPS,self_contribution_c)                                                 161
## cor(subclusterSS,self_contribution_c)                                                 140
## cor(Intercept,subclusterConc_an:self_contribution_c)                                  197
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c)                          112
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c)                           46
## cor(subclusterEM,subclusterConc_an:self_contribution_c)                               367
## cor(subclusterPS,subclusterConc_an:self_contribution_c)                                52
## cor(subclusterSS,subclusterConc_an:self_contribution_c)                                54
## cor(self_contribution_c,subclusterConc_an:self_contribution_c)                         57
## cor(Intercept,subclusterConc_in:self_contribution_c)                                  198
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c)                          427
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c)                          243
## cor(subclusterEM,subclusterConc_in:self_contribution_c)                                37
## cor(subclusterPS,subclusterConc_in:self_contribution_c)                                63
## cor(subclusterSS,subclusterConc_in:self_contribution_c)                               186
## cor(self_contribution_c,subclusterConc_in:self_contribution_c)                        244
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c)      386
## cor(Intercept,subclusterEM:self_contribution_c)                                       401
## cor(subclusterConc_an,subclusterEM:self_contribution_c)                                21
## cor(subclusterConc_in,subclusterEM:self_contribution_c)                                14
## cor(subclusterEM,subclusterEM:self_contribution_c)                                    293
## cor(subclusterPS,subclusterEM:self_contribution_c)                                    137
## cor(subclusterSS,subclusterEM:self_contribution_c)                                     87
## cor(self_contribution_c,subclusterEM:self_contribution_c)                              52
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c)           155
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c)           439
## cor(Intercept,subclusterPS:self_contribution_c)                                       214
## cor(subclusterConc_an,subclusterPS:self_contribution_c)                               119
## cor(subclusterConc_in,subclusterPS:self_contribution_c)                               112
## cor(subclusterEM,subclusterPS:self_contribution_c)                                     43
## cor(subclusterPS,subclusterPS:self_contribution_c)                                     89
## cor(subclusterSS,subclusterPS:self_contribution_c)                                     20
## cor(self_contribution_c,subclusterPS:self_contribution_c)                             282
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c)            56
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c)            99
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)                162
## cor(Intercept,subclusterSS:self_contribution_c)                                        56
## cor(subclusterConc_an,subclusterSS:self_contribution_c)                               220
## cor(subclusterConc_in,subclusterSS:self_contribution_c)                               143
## cor(subclusterEM,subclusterSS:self_contribution_c)                                     81
## cor(subclusterPS,subclusterSS:self_contribution_c)                                    154
## cor(subclusterSS,subclusterSS:self_contribution_c)                                    102
## cor(self_contribution_c,subclusterSS:self_contribution_c)                             152
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c)           151
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c)            44
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)                109
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)                126
## 
## ~word (Number of levels: 32) 
##                                    Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                          0.05      0.02     0.01     0.10 1.19
## sd(self_contribution_c)                0.00      0.00     0.00     0.01 1.43
## cor(Intercept,self_contribution_c)     0.11      0.59    -0.99     0.95 1.70
##                                    Bulk_ESS Tail_ESS
## sd(Intercept)                            16      137
## sd(self_contribution_c)                   8       45
## cor(Intercept,self_contribution_c)        9       14
## 
## Population-Level Effects: 
##                                       Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept                                 1.01      0.08     0.85     1.14 1.22
## phi_Intercept                             3.39      0.31     2.93     3.90 1.43
## subclusterConc_an                        -0.06      0.08    -0.21     0.09 1.20
## subclusterConc_in                        -0.07      0.06    -0.19     0.08 1.30
## subclusterEM                             -0.04      0.08    -0.15     0.13 1.21
## subclusterPS                             -0.01      0.08    -0.18     0.18 1.40
## subclusterSS                             -0.04      0.06    -0.16     0.09 1.37
## self_contribution_c                       0.01      0.00     0.01     0.02 1.32
## difficulty_c                             -0.01      0.00    -0.01    -0.01 1.23
## subclusterConc_an:self_contribution_c    -0.00      0.00    -0.01     0.00 1.23
## subclusterConc_in:self_contribution_c    -0.00      0.00    -0.01     0.00 1.30
## subclusterEM:self_contribution_c         -0.00      0.00    -0.01     0.00 1.22
## subclusterPS:self_contribution_c         -0.00      0.01    -0.01     0.00 1.41
## subclusterSS:self_contribution_c         -0.01      0.00    -0.01     0.00 1.29
## phi_subclusterConc_an                    -0.04      0.28    -0.49     0.45 1.30
## phi_subclusterConc_in                     0.23      0.32    -0.25     0.76 1.38
## phi_subclusterEM                          0.63      0.40     0.07     1.39 1.42
## phi_subclusterPS                          0.89      1.05    -0.55     2.62 1.74
## phi_subclusterSS                          9.04      5.54     1.06    16.71 2.25
##                                       Bulk_ESS Tail_ESS
## Intercept                                   14      139
## phi_Intercept                                9       95
## subclusterConc_an                           15       63
## subclusterConc_in                           25      121
## subclusterEM                                13       61
## subclusterPS                                15       22
## subclusterSS                                52      171
## self_contribution_c                         23      125
## difficulty_c                                33      161
## subclusterConc_an:self_contribution_c       64      170
## subclusterConc_in:self_contribution_c      190      128
## subclusterEM:self_contribution_c            33      118
## subclusterPS:self_contribution_c             8       24
## subclusterSS:self_contribution_c            11      143
## phi_subclusterConc_an                       11      155
## phi_subclusterConc_in                        9       70
## phi_subclusterEM                             8       94
## phi_subclusterPS                             6       37
## phi_subclusterSS                             5       17
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(subcluster_dist_self_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.01         0    -0.01    -0.01        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_self_mdl,
           'self_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0     0.01         0     0.01     0.02       5999
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_self_mdl,
           'subclusterConc_an:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_a... < 0        0         0    -0.01        0       9.64
##   Post.Prob Star
## 1      0.91     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_self_mdl,
           'subclusterConc_in:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_i... < 0        0         0    -0.01        0       6.27
##   Post.Prob Star
## 1      0.86     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_self_mdl,
           'subclusterEM:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:sel... < 0        0         0    -0.01        0       4.39
##   Post.Prob Star
## 1      0.81     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_self_mdl,
           'subclusterPS:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:sel... < 0        0      0.01    -0.01        0       2.13
##   Post.Prob Star
## 1      0.68     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(subcluster_dist_self_mdl,
           'subclusterSS:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:sel... < 0    -0.01         0    -0.01        0      15.64
##   Post.Prob Star
## 1      0.94     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

15 Subcluster analysis of abstract concepts only

Let’s perform models just focusing on the abstract concepts only, since the hypothesis about the different subclusters is really only about abstract concepts.

IOS_subset_other_mdl <- brm(IOS ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        other_contribution_c +
                        difficulty_c +
                        subcluster:other_contribution_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           other_contribution_c +
                           subcluster:other_contribution_c|participant) +
                        (1 + other_contribution_c|word),
           
                      data = filter(df, category == 'abstract'),
                      family = cumulative,
           
                      # MCMC settings:
                               
                      seed = 42,
                      cores = 4,
                      iter = 6000,
                      warmup = 3000,
                      save_pars = save_pars(all = TRUE), # for bayes factors
                      control = list(adapt_delta = 0.99))

# Save model:

save(IOS_subset_other_mdl,
     file = '../models_E2/IOS_subset_other_mdl.Rdata')

Corresponding null model:

IOS_subset_null_mdl <- brm(IOS ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        other_contribution_c +
                        difficulty_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           other_contribution_c +
                           subcluster:other_contribution_c|participant) +
                        (1 + other_contribution_c|word),
           
                      data = filter(df, category == 'abstract'),
                      family = cumulative,
           
                      # MCMC settings:
                               
                      seed = 42,
                      cores = 4,
                      iter = 6000,
                      warmup = 3000,
                      save_pars = save_pars(all = TRUE), # for bayes factors
                      control = list(adapt_delta = 0.99))

# Save model:

save(IOS_subset_null_mdl,
     file = '../models_E2/IOS_subset_null_mdl.Rdata')

Load model:

load('../models_E2/IOS_subset_other_mdl.Rdata')
load('../models_E2/IOS_subset_null_mdl.Rdata')

Show priors:

prior_summary(IOS_subset_other_mdl)
##                 prior     class                              coef       group
##                (flat)         b                                              
##                (flat)         b                      difficulty_c            
##                (flat)         b              other_contribution_c            
##                (flat)         b                      subclusterEM            
##                (flat)         b subclusterEM:other_contribution_c            
##                (flat)         b                      subclusterPS            
##                (flat)         b subclusterPS:other_contribution_c            
##                (flat)         b                      subclusterSS            
##                (flat)         b subclusterSS:other_contribution_c            
##  student_t(3, 0, 2.5) Intercept                                              
##  student_t(3, 0, 2.5) Intercept                                 1            
##  student_t(3, 0, 2.5) Intercept                                 2            
##  student_t(3, 0, 2.5) Intercept                                 3            
##  student_t(3, 0, 2.5) Intercept                                 4            
##  student_t(3, 0, 2.5) Intercept                                 5            
##  lkj_corr_cholesky(1)         L                                              
##  lkj_corr_cholesky(1)         L                                   participant
##  lkj_corr_cholesky(1)         L                                          word
##  student_t(3, 0, 2.5)        sd                                              
##  student_t(3, 0, 2.5)        sd                                   participant
##  student_t(3, 0, 2.5)        sd                         Intercept participant
##  student_t(3, 0, 2.5)        sd              other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterEM participant
##  student_t(3, 0, 2.5)        sd subclusterEM:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterPS participant
##  student_t(3, 0, 2.5)        sd subclusterPS:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterSS participant
##  student_t(3, 0, 2.5)        sd subclusterSS:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                                          word
##  student_t(3, 0, 2.5)        sd                         Intercept        word
##  student_t(3, 0, 2.5)        sd              other_contribution_c        word
##  resp dpar nlpar lb ub       source
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##                        (vectorized)
##                        (vectorized)
##                   0         default
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
prior_summary(IOS_subset_null_mdl)
##                 prior     class                              coef       group
##                (flat)         b                                              
##                (flat)         b                      difficulty_c            
##                (flat)         b              other_contribution_c            
##                (flat)         b                      subclusterEM            
##                (flat)         b                      subclusterPS            
##                (flat)         b                      subclusterSS            
##  student_t(3, 0, 2.5) Intercept                                              
##  student_t(3, 0, 2.5) Intercept                                 1            
##  student_t(3, 0, 2.5) Intercept                                 2            
##  student_t(3, 0, 2.5) Intercept                                 3            
##  student_t(3, 0, 2.5) Intercept                                 4            
##  student_t(3, 0, 2.5) Intercept                                 5            
##  lkj_corr_cholesky(1)         L                                              
##  lkj_corr_cholesky(1)         L                                   participant
##  lkj_corr_cholesky(1)         L                                          word
##  student_t(3, 0, 2.5)        sd                                              
##  student_t(3, 0, 2.5)        sd                                   participant
##  student_t(3, 0, 2.5)        sd                         Intercept participant
##  student_t(3, 0, 2.5)        sd              other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterEM participant
##  student_t(3, 0, 2.5)        sd subclusterEM:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterPS participant
##  student_t(3, 0, 2.5)        sd subclusterPS:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterSS participant
##  student_t(3, 0, 2.5)        sd subclusterSS:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                                          word
##  student_t(3, 0, 2.5)        sd                         Intercept        word
##  student_t(3, 0, 2.5)        sd              other_contribution_c        word
##  resp dpar nlpar lb ub       source
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##                        (vectorized)
##                        (vectorized)
##                   0         default
##                   0    (vectorized)
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##                   0    (vectorized)
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##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)

Bayes factors for both:

# Compute Bayes factor:

IOS_subset_bf <- bayes_factor(IOS_subset_other_mdl, IOS_subset_null_mdl)

# Save:

save(IOS_subset_bf,
     file = '../models_E2/IOS_subset_bf.RData')

Show Bayes factor:

# Load:

load('../models_E2/IOS_subset_bf.RData')

# Show:

IOS_subset_bf
## Estimated Bayes factor in favor of IOS_subset_other_mdl over IOS_subset_null_mdl: 0.00000

Check posterior predictive checks of the mixed beta regression:

pp_check(IOS_subset_other_mdl, ndraws = 100)

Check this model:

IOS_subset_other_mdl
##  Family: cumulative 
##   Links: mu = logit; disc = identity 
## Formula: IOS ~ 1 + subcluster + other_contribution_c + difficulty_c + subcluster:other_contribution_c + (1 + subcluster + other_contribution_c + subcluster:other_contribution_c | participant) + (1 + other_contribution_c | word) 
##    Data: filter(df, category == "abstract") (Number of observations: 516) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                          Estimate
## sd(Intercept)                                                                3.03
## sd(subclusterEM)                                                             0.60
## sd(subclusterPS)                                                             0.51
## sd(subclusterSS)                                                             0.83
## sd(other_contribution_c)                                                     0.07
## sd(subclusterEM:other_contribution_c)                                        0.06
## sd(subclusterPS:other_contribution_c)                                        0.04
## sd(subclusterSS:other_contribution_c)                                        0.04
## cor(Intercept,subclusterEM)                                                 -0.05
## cor(Intercept,subclusterPS)                                                  0.01
## cor(subclusterEM,subclusterPS)                                               0.05
## cor(Intercept,subclusterSS)                                                 -0.10
## cor(subclusterEM,subclusterSS)                                              -0.00
## cor(subclusterPS,subclusterSS)                                              -0.00
## cor(Intercept,other_contribution_c)                                         -0.04
## cor(subclusterEM,other_contribution_c)                                      -0.10
## cor(subclusterPS,other_contribution_c)                                       0.01
## cor(subclusterSS,other_contribution_c)                                       0.15
## cor(Intercept,subclusterEM:other_contribution_c)                            -0.01
## cor(subclusterEM,subclusterEM:other_contribution_c)                          0.04
## cor(subclusterPS,subclusterEM:other_contribution_c)                         -0.11
## cor(subclusterSS,subclusterEM:other_contribution_c)                          0.03
## cor(other_contribution_c,subclusterEM:other_contribution_c)                 -0.09
## cor(Intercept,subclusterPS:other_contribution_c)                             0.19
## cor(subclusterEM,subclusterPS:other_contribution_c)                         -0.10
## cor(subclusterPS,subclusterPS:other_contribution_c)                         -0.01
## cor(subclusterSS,subclusterPS:other_contribution_c)                          0.06
## cor(other_contribution_c,subclusterPS:other_contribution_c)                 -0.03
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)     0.01
## cor(Intercept,subclusterSS:other_contribution_c)                             0.12
## cor(subclusterEM,subclusterSS:other_contribution_c)                          0.02
## cor(subclusterPS,subclusterSS:other_contribution_c)                          0.05
## cor(subclusterSS,subclusterSS:other_contribution_c)                         -0.10
## cor(other_contribution_c,subclusterSS:other_contribution_c)                  0.07
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)     0.11
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)     0.10
##                                                                          Est.Error
## sd(Intercept)                                                                 0.36
## sd(subclusterEM)                                                              0.44
## sd(subclusterPS)                                                              0.39
## sd(subclusterSS)                                                              0.53
## sd(other_contribution_c)                                                      0.02
## sd(subclusterEM:other_contribution_c)                                         0.03
## sd(subclusterPS:other_contribution_c)                                         0.03
## sd(subclusterSS:other_contribution_c)                                         0.03
## cor(Intercept,subclusterEM)                                                   0.29
## cor(Intercept,subclusterPS)                                                   0.30
## cor(subclusterEM,subclusterPS)                                                0.33
## cor(Intercept,subclusterSS)                                                   0.28
## cor(subclusterEM,subclusterSS)                                                0.32
## cor(subclusterPS,subclusterSS)                                                0.33
## cor(Intercept,other_contribution_c)                                           0.20
## cor(subclusterEM,other_contribution_c)                                        0.32
## cor(subclusterPS,other_contribution_c)                                        0.32
## cor(subclusterSS,other_contribution_c)                                        0.31
## cor(Intercept,subclusterEM:other_contribution_c)                              0.25
## cor(subclusterEM,subclusterEM:other_contribution_c)                           0.33
## cor(subclusterPS,subclusterEM:other_contribution_c)                           0.33
## cor(subclusterSS,subclusterEM:other_contribution_c)                           0.32
## cor(other_contribution_c,subclusterEM:other_contribution_c)                   0.30
## cor(Intercept,subclusterPS:other_contribution_c)                              0.28
## cor(subclusterEM,subclusterPS:other_contribution_c)                           0.33
## cor(subclusterPS,subclusterPS:other_contribution_c)                           0.33
## cor(subclusterSS,subclusterPS:other_contribution_c)                           0.33
## cor(other_contribution_c,subclusterPS:other_contribution_c)                   0.31
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)      0.31
## cor(Intercept,subclusterSS:other_contribution_c)                              0.30
## cor(subclusterEM,subclusterSS:other_contribution_c)                           0.33
## cor(subclusterPS,subclusterSS:other_contribution_c)                           0.33
## cor(subclusterSS,subclusterSS:other_contribution_c)                           0.33
## cor(other_contribution_c,subclusterSS:other_contribution_c)                   0.32
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)      0.32
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)      0.33
##                                                                          l-95% CI
## sd(Intercept)                                                                2.39
## sd(subclusterEM)                                                             0.02
## sd(subclusterPS)                                                             0.02
## sd(subclusterSS)                                                             0.04
## sd(other_contribution_c)                                                     0.02
## sd(subclusterEM:other_contribution_c)                                        0.01
## sd(subclusterPS:other_contribution_c)                                        0.00
## sd(subclusterSS:other_contribution_c)                                        0.00
## cor(Intercept,subclusterEM)                                                 -0.58
## cor(Intercept,subclusterPS)                                                 -0.58
## cor(subclusterEM,subclusterPS)                                              -0.59
## cor(Intercept,subclusterSS)                                                 -0.62
## cor(subclusterEM,subclusterSS)                                              -0.63
## cor(subclusterPS,subclusterSS)                                              -0.63
## cor(Intercept,other_contribution_c)                                         -0.42
## cor(subclusterEM,other_contribution_c)                                      -0.68
## cor(subclusterPS,other_contribution_c)                                      -0.61
## cor(subclusterSS,other_contribution_c)                                      -0.49
## cor(Intercept,subclusterEM:other_contribution_c)                            -0.50
## cor(subclusterEM,subclusterEM:other_contribution_c)                         -0.60
## cor(subclusterPS,subclusterEM:other_contribution_c)                         -0.70
## cor(subclusterSS,subclusterEM:other_contribution_c)                         -0.60
## cor(other_contribution_c,subclusterEM:other_contribution_c)                 -0.61
## cor(Intercept,subclusterPS:other_contribution_c)                            -0.41
## cor(subclusterEM,subclusterPS:other_contribution_c)                         -0.70
## cor(subclusterPS,subclusterPS:other_contribution_c)                         -0.62
## cor(subclusterSS,subclusterPS:other_contribution_c)                         -0.57
## cor(other_contribution_c,subclusterPS:other_contribution_c)                 -0.61
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)    -0.59
## cor(Intercept,subclusterSS:other_contribution_c)                            -0.50
## cor(subclusterEM,subclusterSS:other_contribution_c)                         -0.61
## cor(subclusterPS,subclusterSS:other_contribution_c)                         -0.59
## cor(subclusterSS,subclusterSS:other_contribution_c)                         -0.70
## cor(other_contribution_c,subclusterSS:other_contribution_c)                 -0.56
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)    -0.55
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)    -0.56
##                                                                          u-95% CI
## sd(Intercept)                                                                3.80
## sd(subclusterEM)                                                             1.64
## sd(subclusterPS)                                                             1.45
## sd(subclusterSS)                                                             1.96
## sd(other_contribution_c)                                                     0.11
## sd(subclusterEM:other_contribution_c)                                        0.11
## sd(subclusterPS:other_contribution_c)                                        0.11
## sd(subclusterSS:other_contribution_c)                                        0.11
## cor(Intercept,subclusterEM)                                                  0.52
## cor(Intercept,subclusterPS)                                                  0.60
## cor(subclusterEM,subclusterPS)                                               0.66
## cor(Intercept,subclusterSS)                                                  0.49
## cor(subclusterEM,subclusterSS)                                               0.62
## cor(subclusterPS,subclusterSS)                                               0.62
## cor(Intercept,other_contribution_c)                                          0.37
## cor(subclusterEM,other_contribution_c)                                       0.56
## cor(subclusterPS,other_contribution_c)                                       0.62
## cor(subclusterSS,other_contribution_c)                                       0.70
## cor(Intercept,subclusterEM:other_contribution_c)                             0.48
## cor(subclusterEM,subclusterEM:other_contribution_c)                          0.65
## cor(subclusterPS,subclusterEM:other_contribution_c)                          0.56
## cor(subclusterSS,subclusterEM:other_contribution_c)                          0.63
## cor(other_contribution_c,subclusterEM:other_contribution_c)                  0.52
## cor(Intercept,subclusterPS:other_contribution_c)                             0.67
## cor(subclusterEM,subclusterPS:other_contribution_c)                          0.57
## cor(subclusterPS,subclusterPS:other_contribution_c)                          0.62
## cor(subclusterSS,subclusterPS:other_contribution_c)                          0.66
## cor(other_contribution_c,subclusterPS:other_contribution_c)                  0.59
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)     0.60
## cor(Intercept,subclusterSS:other_contribution_c)                             0.66
## cor(subclusterEM,subclusterSS:other_contribution_c)                          0.65
## cor(subclusterPS,subclusterSS:other_contribution_c)                          0.67
## cor(subclusterSS,subclusterSS:other_contribution_c)                          0.55
## cor(other_contribution_c,subclusterSS:other_contribution_c)                  0.67
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)     0.68
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)     0.68
##                                                                          Rhat
## sd(Intercept)                                                            1.00
## sd(subclusterEM)                                                         1.00
## sd(subclusterPS)                                                         1.00
## sd(subclusterSS)                                                         1.00
## sd(other_contribution_c)                                                 1.00
## sd(subclusterEM:other_contribution_c)                                    1.00
## sd(subclusterPS:other_contribution_c)                                    1.00
## sd(subclusterSS:other_contribution_c)                                    1.00
## cor(Intercept,subclusterEM)                                              1.00
## cor(Intercept,subclusterPS)                                              1.00
## cor(subclusterEM,subclusterPS)                                           1.00
## cor(Intercept,subclusterSS)                                              1.00
## cor(subclusterEM,subclusterSS)                                           1.00
## cor(subclusterPS,subclusterSS)                                           1.00
## cor(Intercept,other_contribution_c)                                      1.00
## cor(subclusterEM,other_contribution_c)                                   1.00
## cor(subclusterPS,other_contribution_c)                                   1.00
## cor(subclusterSS,other_contribution_c)                                   1.00
## cor(Intercept,subclusterEM:other_contribution_c)                         1.00
## cor(subclusterEM,subclusterEM:other_contribution_c)                      1.00
## cor(subclusterPS,subclusterEM:other_contribution_c)                      1.00
## cor(subclusterSS,subclusterEM:other_contribution_c)                      1.00
## cor(other_contribution_c,subclusterEM:other_contribution_c)              1.00
## cor(Intercept,subclusterPS:other_contribution_c)                         1.00
## cor(subclusterEM,subclusterPS:other_contribution_c)                      1.00
## cor(subclusterPS,subclusterPS:other_contribution_c)                      1.00
## cor(subclusterSS,subclusterPS:other_contribution_c)                      1.00
## cor(other_contribution_c,subclusterPS:other_contribution_c)              1.00
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(Intercept,subclusterSS:other_contribution_c)                         1.00
## cor(subclusterEM,subclusterSS:other_contribution_c)                      1.00
## cor(subclusterPS,subclusterSS:other_contribution_c)                      1.00
## cor(subclusterSS,subclusterSS:other_contribution_c)                      1.00
## cor(other_contribution_c,subclusterSS:other_contribution_c)              1.00
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 1.00
##                                                                          Bulk_ESS
## sd(Intercept)                                                                1818
## sd(subclusterEM)                                                             1564
## sd(subclusterPS)                                                             2120
## sd(subclusterSS)                                                             1698
## sd(other_contribution_c)                                                     1449
## sd(subclusterEM:other_contribution_c)                                        1469
## sd(subclusterPS:other_contribution_c)                                        1821
## sd(subclusterSS:other_contribution_c)                                        2099
## cor(Intercept,subclusterEM)                                                 10633
## cor(Intercept,subclusterPS)                                                 14051
## cor(subclusterEM,subclusterPS)                                               6581
## cor(Intercept,subclusterSS)                                                 11480
## cor(subclusterEM,subclusterSS)                                               5209
## cor(subclusterPS,subclusterSS)                                               4938
## cor(Intercept,other_contribution_c)                                          6603
## cor(subclusterEM,other_contribution_c)                                       1470
## cor(subclusterPS,other_contribution_c)                                       1488
## cor(subclusterSS,other_contribution_c)                                       1815
## cor(Intercept,subclusterEM:other_contribution_c)                             7336
## cor(subclusterEM,subclusterEM:other_contribution_c)                          3126
## cor(subclusterPS,subclusterEM:other_contribution_c)                          3473
## cor(subclusterSS,subclusterEM:other_contribution_c)                          4037
## cor(other_contribution_c,subclusterEM:other_contribution_c)                  4514
## cor(Intercept,subclusterPS:other_contribution_c)                             9979
## cor(subclusterEM,subclusterPS:other_contribution_c)                          4604
## cor(subclusterPS,subclusterPS:other_contribution_c)                          5752
## cor(subclusterSS,subclusterPS:other_contribution_c)                          6232
## cor(other_contribution_c,subclusterPS:other_contribution_c)                  7841
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)     7002
## cor(Intercept,subclusterSS:other_contribution_c)                             9519
## cor(subclusterEM,subclusterSS:other_contribution_c)                          5357
## cor(subclusterPS,subclusterSS:other_contribution_c)                          6596
## cor(subclusterSS,subclusterSS:other_contribution_c)                          6333
## cor(other_contribution_c,subclusterSS:other_contribution_c)                  7314
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)     7636
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)     6121
##                                                                          Tail_ESS
## sd(Intercept)                                                                4137
## sd(subclusterEM)                                                             2671
## sd(subclusterPS)                                                             3652
## sd(subclusterSS)                                                             4249
## sd(other_contribution_c)                                                     2108
## sd(subclusterEM:other_contribution_c)                                        2074
## sd(subclusterPS:other_contribution_c)                                        3718
## sd(subclusterSS:other_contribution_c)                                        4182
## cor(Intercept,subclusterEM)                                                  7870
## cor(Intercept,subclusterPS)                                                  8116
## cor(subclusterEM,subclusterPS)                                               8254
## cor(Intercept,subclusterSS)                                                  7967
## cor(subclusterEM,subclusterSS)                                               6700
## cor(subclusterPS,subclusterSS)                                               8192
## cor(Intercept,other_contribution_c)                                          7402
## cor(subclusterEM,other_contribution_c)                                       3365
## cor(subclusterPS,other_contribution_c)                                       3578
## cor(subclusterSS,other_contribution_c)                                       3580
## cor(Intercept,subclusterEM:other_contribution_c)                             7347
## cor(subclusterEM,subclusterEM:other_contribution_c)                          6182
## cor(subclusterPS,subclusterEM:other_contribution_c)                          6589
## cor(subclusterSS,subclusterEM:other_contribution_c)                          7273
## cor(other_contribution_c,subclusterEM:other_contribution_c)                  7826
## cor(Intercept,subclusterPS:other_contribution_c)                             6866
## cor(subclusterEM,subclusterPS:other_contribution_c)                          8185
## cor(subclusterPS,subclusterPS:other_contribution_c)                          8167
## cor(subclusterSS,subclusterPS:other_contribution_c)                          8675
## cor(other_contribution_c,subclusterPS:other_contribution_c)                  9157
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)     8838
## cor(Intercept,subclusterSS:other_contribution_c)                             8336
## cor(subclusterEM,subclusterSS:other_contribution_c)                          8390
## cor(subclusterPS,subclusterSS:other_contribution_c)                          9026
## cor(subclusterSS,subclusterSS:other_contribution_c)                          8586
## cor(other_contribution_c,subclusterSS:other_contribution_c)                  7682
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)     9120
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)     9647
## 
## ~word (Number of levels: 16) 
##                                     Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                           0.24      0.18     0.01     0.69 1.00
## sd(other_contribution_c)                0.02      0.01     0.00     0.05 1.00
## cor(Intercept,other_contribution_c)    -0.07      0.57    -0.95     0.93 1.00
##                                     Bulk_ESS Tail_ESS
## sd(Intercept)                           3998     5608
## sd(other_contribution_c)                2133     4121
## cor(Intercept,other_contribution_c)     4907     7558
## 
## Population-Level Effects: 
##                                   Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1]                         -6.40      0.66    -7.79    -5.22 1.00
## Intercept[2]                         -2.07      0.41    -2.92    -1.30 1.00
## Intercept[3]                          1.03      0.40     0.26     1.82 1.00
## Intercept[4]                          3.66      0.49     2.75     4.66 1.00
## Intercept[5]                          6.97      0.70     5.71     8.45 1.00
## subclusterEM                          0.10      0.35    -0.59     0.79 1.00
## subclusterPS                         -0.02      0.36    -0.75     0.71 1.00
## subclusterSS                         -0.16      0.41    -0.97     0.62 1.00
## other_contribution_c                  0.06      0.02     0.02     0.10 1.00
## difficulty_c                         -0.03      0.01    -0.05    -0.02 1.00
## subclusterEM:other_contribution_c    -0.00      0.02    -0.05     0.04 1.00
## subclusterPS:other_contribution_c     0.01      0.02    -0.04     0.06 1.00
## subclusterSS:other_contribution_c     0.01      0.03    -0.05     0.06 1.00
##                                   Bulk_ESS Tail_ESS
## Intercept[1]                          2502     4652
## Intercept[2]                          4068     6607
## Intercept[3]                          4545     5839
## Intercept[4]                          3134     4861
## Intercept[5]                          2489     3839
## subclusterEM                          7697     6938
## subclusterPS                          8642     7728
## subclusterSS                          6904     6589
## other_contribution_c                  4740     5337
## difficulty_c                          6602     8466
## subclusterEM:other_contribution_c     6370     5583
## subclusterPS:other_contribution_c     6021     5908
## subclusterSS:other_contribution_c     6001     6151
## 
## Family Specific Parameters: 
##      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc     1.00      0.00     1.00     1.00   NA       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(IOS_subset_other_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.03      0.01    -0.04    -0.02        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_subset_other_mdl,
           'other_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0     0.06      0.02     0.03     0.09     427.57
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_subset_other_mdl,
           'subclusterEM:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:oth... < 0        0      0.02    -0.04     0.03       1.25
##   Post.Prob Star
## 1      0.56     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_subset_other_mdl,
           'subclusterPS:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:oth... < 0     0.01      0.02    -0.03     0.05       0.43
##   Post.Prob Star
## 1       0.3     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_subset_other_mdl,
           'subclusterSS:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:oth... < 0     0.01      0.03    -0.03     0.05       0.51
##   Post.Prob Star
## 1      0.34     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Next, the model with IOS on self contribution:

IOS_subset_self_mdl <- brm(IOS ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        self_contribution_c +
                        difficulty_c +
                        subcluster:self_contribution_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           self_contribution_c +
                           subcluster:self_contribution_c|participant) +
                        (1 + self_contribution_c|word),
           
                      data = filter(df, category == 'abstract'),
                      family = cumulative,
           
                      # MCMC settings:
                               
                      seed = 42,
                      cores = 4,
                      iter = 6000,
                      warmup = 3000,
                      save_pars = save_pars(all = TRUE), # for bayes factors
                      control = list(adapt_delta = 0.99))

# Save model:

save(IOS_subset_self_mdl,
     file = '../models_E2/IOS_subset_self_mdl.Rdata')

Corresponding null model:

IOS_subset_self_null <- brm(IOS ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        self_contribution_c +
                        difficulty_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           self_contribution_c +
                           subcluster:self_contribution_c|participant) +
                        (1 + self_contribution_c|word),
           
                      data = filter(df, category == 'abstract'),
                      family = cumulative,
           
                      # MCMC settings:
                               
                      seed = 42,
                      cores = 4,
                      iter = 6000,
                      warmup = 3000,
                      save_pars = save_pars(all = TRUE), # for bayes factors
                      control = list(adapt_delta = 0.99))

# Save model:

save(IOS_subset_self_null,
     file = '../models_E2/IOS_subset_self_null.RData')

Load model:

load('../models_E2/IOS_subset_self_mdl.Rdata')
load('../models_E2/IOS_subset_self_null.RData')

Show priors:

prior_summary(IOS_subset_self_mdl)
##                 prior     class                             coef       group
##                (flat)         b                                             
##                (flat)         b                     difficulty_c            
##                (flat)         b              self_contribution_c            
##                (flat)         b                     subclusterEM            
##                (flat)         b subclusterEM:self_contribution_c            
##                (flat)         b                     subclusterPS            
##                (flat)         b subclusterPS:self_contribution_c            
##                (flat)         b                     subclusterSS            
##                (flat)         b subclusterSS:self_contribution_c            
##  student_t(3, 0, 2.5) Intercept                                             
##  student_t(3, 0, 2.5) Intercept                                1            
##  student_t(3, 0, 2.5) Intercept                                2            
##  student_t(3, 0, 2.5) Intercept                                3            
##  student_t(3, 0, 2.5) Intercept                                4            
##  student_t(3, 0, 2.5) Intercept                                5            
##  lkj_corr_cholesky(1)         L                                             
##  lkj_corr_cholesky(1)         L                                  participant
##  lkj_corr_cholesky(1)         L                                         word
##  student_t(3, 0, 2.5)        sd                                             
##  student_t(3, 0, 2.5)        sd                                  participant
##  student_t(3, 0, 2.5)        sd                        Intercept participant
##  student_t(3, 0, 2.5)        sd              self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterEM participant
##  student_t(3, 0, 2.5)        sd subclusterEM:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterPS participant
##  student_t(3, 0, 2.5)        sd subclusterPS:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterSS participant
##  student_t(3, 0, 2.5)        sd subclusterSS:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                                         word
##  student_t(3, 0, 2.5)        sd                        Intercept        word
##  student_t(3, 0, 2.5)        sd              self_contribution_c        word
##  resp dpar nlpar lb ub       source
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##                        (vectorized)
##                        (vectorized)
##                   0         default
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
prior_summary(IOS_subset_self_null)
##                 prior     class                             coef       group
##                (flat)         b                                             
##                (flat)         b                     difficulty_c            
##                (flat)         b              self_contribution_c            
##                (flat)         b                     subclusterEM            
##                (flat)         b                     subclusterPS            
##                (flat)         b                     subclusterSS            
##  student_t(3, 0, 2.5) Intercept                                             
##  student_t(3, 0, 2.5) Intercept                                1            
##  student_t(3, 0, 2.5) Intercept                                2            
##  student_t(3, 0, 2.5) Intercept                                3            
##  student_t(3, 0, 2.5) Intercept                                4            
##  student_t(3, 0, 2.5) Intercept                                5            
##  lkj_corr_cholesky(1)         L                                             
##  lkj_corr_cholesky(1)         L                                  participant
##  lkj_corr_cholesky(1)         L                                         word
##  student_t(3, 0, 2.5)        sd                                             
##  student_t(3, 0, 2.5)        sd                                  participant
##  student_t(3, 0, 2.5)        sd                        Intercept participant
##  student_t(3, 0, 2.5)        sd              self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterEM participant
##  student_t(3, 0, 2.5)        sd subclusterEM:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterPS participant
##  student_t(3, 0, 2.5)        sd subclusterPS:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterSS participant
##  student_t(3, 0, 2.5)        sd subclusterSS:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                                         word
##  student_t(3, 0, 2.5)        sd                        Intercept        word
##  student_t(3, 0, 2.5)        sd              self_contribution_c        word
##  resp dpar nlpar lb ub       source
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##                        (vectorized)
##                        (vectorized)
##                   0         default
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)

Bayes factors for both:

# Compute Bayes factor:

IOS_subset_self_bf <- bayes_factor(IOS_subset_self_mdl, IOS_subset_self_null)

# Save:

save(IOS_subset_self_bf,
     file = '../models_E2/IOS_subset_self_bf.RData')

Show Bayes factor:

# Load:

load('../models_E2/IOS_subset_self_bf.RData')

# Show:

IOS_subset_self_bf
## Estimated Bayes factor in favor of IOS_subset_self_mdl over IOS_subset_self_null: 0.00000

Check posterior predictive checks of the mixed beta regression:

pp_check(IOS_subset_self_mdl, ndraws = 100)

Check this model:

IOS_subset_self_mdl
##  Family: cumulative 
##   Links: mu = logit; disc = identity 
## Formula: IOS ~ 1 + subcluster + self_contribution_c + difficulty_c + subcluster:self_contribution_c + (1 + subcluster + self_contribution_c + subcluster:self_contribution_c | participant) + (1 + self_contribution_c | word) 
##    Data: filter(df, category == "abstract") (Number of observations: 516) 
##   Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
##          total post-warmup draws = 12000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                        Estimate
## sd(Intercept)                                                              2.94
## sd(subclusterEM)                                                           0.56
## sd(subclusterPS)                                                           0.73
## sd(subclusterSS)                                                           0.52
## sd(self_contribution_c)                                                    0.04
## sd(subclusterEM:self_contribution_c)                                       0.03
## sd(subclusterPS:self_contribution_c)                                       0.03
## sd(subclusterSS:self_contribution_c)                                       0.05
## cor(Intercept,subclusterEM)                                               -0.04
## cor(Intercept,subclusterPS)                                                0.04
## cor(subclusterEM,subclusterPS)                                             0.01
## cor(Intercept,subclusterSS)                                                0.03
## cor(subclusterEM,subclusterSS)                                             0.03
## cor(subclusterPS,subclusterSS)                                             0.04
## cor(Intercept,self_contribution_c)                                         0.19
## cor(subclusterEM,self_contribution_c)                                     -0.01
## cor(subclusterPS,self_contribution_c)                                      0.05
## cor(subclusterSS,self_contribution_c)                                      0.07
## cor(Intercept,subclusterEM:self_contribution_c)                            0.12
## cor(subclusterEM,subclusterEM:self_contribution_c)                         0.07
## cor(subclusterPS,subclusterEM:self_contribution_c)                        -0.09
## cor(subclusterSS,subclusterEM:self_contribution_c)                         0.04
## cor(self_contribution_c,subclusterEM:self_contribution_c)                 -0.15
## cor(Intercept,subclusterPS:self_contribution_c)                            0.06
## cor(subclusterEM,subclusterPS:self_contribution_c)                        -0.11
## cor(subclusterPS,subclusterPS:self_contribution_c)                         0.08
## cor(subclusterSS,subclusterPS:self_contribution_c)                        -0.01
## cor(self_contribution_c,subclusterPS:self_contribution_c)                  0.02
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)     0.00
## cor(Intercept,subclusterSS:self_contribution_c)                            0.09
## cor(subclusterEM,subclusterSS:self_contribution_c)                         0.00
## cor(subclusterPS,subclusterSS:self_contribution_c)                        -0.00
## cor(subclusterSS,subclusterSS:self_contribution_c)                        -0.05
## cor(self_contribution_c,subclusterSS:self_contribution_c)                  0.02
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)     0.01
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)     0.04
##                                                                        Est.Error
## sd(Intercept)                                                               0.33
## sd(subclusterEM)                                                            0.40
## sd(subclusterPS)                                                            0.51
## sd(subclusterSS)                                                            0.39
## sd(self_contribution_c)                                                     0.02
## sd(subclusterEM:self_contribution_c)                                        0.02
## sd(subclusterPS:self_contribution_c)                                        0.02
## sd(subclusterSS:self_contribution_c)                                        0.03
## cor(Intercept,subclusterEM)                                                 0.29
## cor(Intercept,subclusterPS)                                                 0.27
## cor(subclusterEM,subclusterPS)                                              0.33
## cor(Intercept,subclusterSS)                                                 0.30
## cor(subclusterEM,subclusterSS)                                              0.33
## cor(subclusterPS,subclusterSS)                                              0.33
## cor(Intercept,self_contribution_c)                                          0.25
## cor(subclusterEM,self_contribution_c)                                       0.33
## cor(subclusterPS,self_contribution_c)                                       0.32
## cor(subclusterSS,self_contribution_c)                                       0.33
## cor(Intercept,subclusterEM:self_contribution_c)                             0.30
## cor(subclusterEM,subclusterEM:self_contribution_c)                          0.33
## cor(subclusterPS,subclusterEM:self_contribution_c)                          0.33
## cor(subclusterSS,subclusterEM:self_contribution_c)                          0.34
## cor(self_contribution_c,subclusterEM:self_contribution_c)                   0.34
## cor(Intercept,subclusterPS:self_contribution_c)                             0.29
## cor(subclusterEM,subclusterPS:self_contribution_c)                          0.34
## cor(subclusterPS,subclusterPS:self_contribution_c)                          0.33
## cor(subclusterSS,subclusterPS:self_contribution_c)                          0.33
## cor(self_contribution_c,subclusterPS:self_contribution_c)                   0.32
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)      0.33
## cor(Intercept,subclusterSS:self_contribution_c)                             0.26
## cor(subclusterEM,subclusterSS:self_contribution_c)                          0.33
## cor(subclusterPS,subclusterSS:self_contribution_c)                          0.32
## cor(subclusterSS,subclusterSS:self_contribution_c)                          0.33
## cor(self_contribution_c,subclusterSS:self_contribution_c)                   0.32
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)      0.32
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)      0.33
##                                                                        l-95% CI
## sd(Intercept)                                                              2.36
## sd(subclusterEM)                                                           0.02
## sd(subclusterPS)                                                           0.03
## sd(subclusterSS)                                                           0.02
## sd(self_contribution_c)                                                    0.00
## sd(subclusterEM:self_contribution_c)                                       0.00
## sd(subclusterPS:self_contribution_c)                                       0.00
## sd(subclusterSS:self_contribution_c)                                       0.00
## cor(Intercept,subclusterEM)                                               -0.57
## cor(Intercept,subclusterPS)                                               -0.51
## cor(subclusterEM,subclusterPS)                                            -0.61
## cor(Intercept,subclusterSS)                                               -0.56
## cor(subclusterEM,subclusterSS)                                            -0.60
## cor(subclusterPS,subclusterSS)                                            -0.61
## cor(Intercept,self_contribution_c)                                        -0.35
## cor(subclusterEM,self_contribution_c)                                     -0.64
## cor(subclusterPS,self_contribution_c)                                     -0.58
## cor(subclusterSS,self_contribution_c)                                     -0.58
## cor(Intercept,subclusterEM:self_contribution_c)                           -0.49
## cor(subclusterEM,subclusterEM:self_contribution_c)                        -0.58
## cor(subclusterPS,subclusterEM:self_contribution_c)                        -0.68
## cor(subclusterSS,subclusterEM:self_contribution_c)                        -0.61
## cor(self_contribution_c,subclusterEM:self_contribution_c)                 -0.73
## cor(Intercept,subclusterPS:self_contribution_c)                           -0.53
## cor(subclusterEM,subclusterPS:self_contribution_c)                        -0.71
## cor(subclusterPS,subclusterPS:self_contribution_c)                        -0.56
## cor(subclusterSS,subclusterPS:self_contribution_c)                        -0.64
## cor(self_contribution_c,subclusterPS:self_contribution_c)                 -0.61
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)    -0.63
## cor(Intercept,subclusterSS:self_contribution_c)                           -0.46
## cor(subclusterEM,subclusterSS:self_contribution_c)                        -0.61
## cor(subclusterPS,subclusterSS:self_contribution_c)                        -0.61
## cor(subclusterSS,subclusterSS:self_contribution_c)                        -0.66
## cor(self_contribution_c,subclusterSS:self_contribution_c)                 -0.59
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)    -0.62
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)    -0.60
##                                                                        u-95% CI
## sd(Intercept)                                                              3.63
## sd(subclusterEM)                                                           1.48
## sd(subclusterPS)                                                           1.87
## sd(subclusterSS)                                                           1.46
## sd(self_contribution_c)                                                    0.08
## sd(subclusterEM:self_contribution_c)                                       0.08
## sd(subclusterPS:self_contribution_c)                                       0.09
## sd(subclusterSS:self_contribution_c)                                       0.11
## cor(Intercept,subclusterEM)                                                0.54
## cor(Intercept,subclusterPS)                                                0.57
## cor(subclusterEM,subclusterPS)                                             0.63
## cor(Intercept,subclusterSS)                                                0.60
## cor(subclusterEM,subclusterSS)                                             0.66
## cor(subclusterPS,subclusterSS)                                             0.65
## cor(Intercept,self_contribution_c)                                         0.65
## cor(subclusterEM,self_contribution_c)                                      0.62
## cor(subclusterPS,self_contribution_c)                                      0.65
## cor(subclusterSS,self_contribution_c)                                      0.67
## cor(Intercept,subclusterEM:self_contribution_c)                            0.66
## cor(subclusterEM,subclusterEM:self_contribution_c)                         0.67
## cor(subclusterPS,subclusterEM:self_contribution_c)                         0.57
## cor(subclusterSS,subclusterEM:self_contribution_c)                         0.66
## cor(self_contribution_c,subclusterEM:self_contribution_c)                  0.54
## cor(Intercept,subclusterPS:self_contribution_c)                            0.59
## cor(subclusterEM,subclusterPS:self_contribution_c)                         0.57
## cor(subclusterPS,subclusterPS:self_contribution_c)                         0.68
## cor(subclusterSS,subclusterPS:self_contribution_c)                         0.62
## cor(self_contribution_c,subclusterPS:self_contribution_c)                  0.64
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)     0.62
## cor(Intercept,subclusterSS:self_contribution_c)                            0.58
## cor(subclusterEM,subclusterSS:self_contribution_c)                         0.63
## cor(subclusterPS,subclusterSS:self_contribution_c)                         0.62
## cor(subclusterSS,subclusterSS:self_contribution_c)                         0.60
## cor(self_contribution_c,subclusterSS:self_contribution_c)                  0.63
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)     0.62
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)     0.66
##                                                                        Rhat
## sd(Intercept)                                                          1.00
## sd(subclusterEM)                                                       1.00
## sd(subclusterPS)                                                       1.00
## sd(subclusterSS)                                                       1.00
## sd(self_contribution_c)                                                1.00
## sd(subclusterEM:self_contribution_c)                                   1.00
## sd(subclusterPS:self_contribution_c)                                   1.00
## sd(subclusterSS:self_contribution_c)                                   1.00
## cor(Intercept,subclusterEM)                                            1.00
## cor(Intercept,subclusterPS)                                            1.00
## cor(subclusterEM,subclusterPS)                                         1.00
## cor(Intercept,subclusterSS)                                            1.00
## cor(subclusterEM,subclusterSS)                                         1.00
## cor(subclusterPS,subclusterSS)                                         1.00
## cor(Intercept,self_contribution_c)                                     1.00
## cor(subclusterEM,self_contribution_c)                                  1.00
## cor(subclusterPS,self_contribution_c)                                  1.00
## cor(subclusterSS,self_contribution_c)                                  1.00
## cor(Intercept,subclusterEM:self_contribution_c)                        1.00
## cor(subclusterEM,subclusterEM:self_contribution_c)                     1.00
## cor(subclusterPS,subclusterEM:self_contribution_c)                     1.00
## cor(subclusterSS,subclusterEM:self_contribution_c)                     1.00
## cor(self_contribution_c,subclusterEM:self_contribution_c)              1.00
## cor(Intercept,subclusterPS:self_contribution_c)                        1.00
## cor(subclusterEM,subclusterPS:self_contribution_c)                     1.00
## cor(subclusterPS,subclusterPS:self_contribution_c)                     1.00
## cor(subclusterSS,subclusterPS:self_contribution_c)                     1.00
## cor(self_contribution_c,subclusterPS:self_contribution_c)              1.00
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(Intercept,subclusterSS:self_contribution_c)                        1.00
## cor(subclusterEM,subclusterSS:self_contribution_c)                     1.00
## cor(subclusterPS,subclusterSS:self_contribution_c)                     1.00
## cor(subclusterSS,subclusterSS:self_contribution_c)                     1.00
## cor(self_contribution_c,subclusterSS:self_contribution_c)              1.00
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 1.00
##                                                                        Bulk_ESS
## sd(Intercept)                                                              1864
## sd(subclusterEM)                                                           1528
## sd(subclusterPS)                                                           1037
## sd(subclusterSS)                                                           2368
## sd(self_contribution_c)                                                     648
## sd(subclusterEM:self_contribution_c)                                       1926
## sd(subclusterPS:self_contribution_c)                                       1939
## sd(subclusterSS:self_contribution_c)                                       1765
## cor(Intercept,subclusterEM)                                               11517
## cor(Intercept,subclusterPS)                                               11296
## cor(subclusterEM,subclusterPS)                                             4209
## cor(Intercept,subclusterSS)                                               12473
## cor(subclusterEM,subclusterSS)                                             7046
## cor(subclusterPS,subclusterSS)                                             7379
## cor(Intercept,self_contribution_c)                                         5771
## cor(subclusterEM,self_contribution_c)                                      2315
## cor(subclusterPS,self_contribution_c)                                      2781
## cor(subclusterSS,self_contribution_c)                                      2488
## cor(Intercept,subclusterEM:self_contribution_c)                            9657
## cor(subclusterEM,subclusterEM:self_contribution_c)                         5512
## cor(subclusterPS,subclusterEM:self_contribution_c)                         5253
## cor(subclusterSS,subclusterEM:self_contribution_c)                         6060
## cor(self_contribution_c,subclusterEM:self_contribution_c)                  4566
## cor(Intercept,subclusterPS:self_contribution_c)                           10887
## cor(subclusterEM,subclusterPS:self_contribution_c)                         4402
## cor(subclusterPS,subclusterPS:self_contribution_c)                         5617
## cor(subclusterSS,subclusterPS:self_contribution_c)                         5975
## cor(self_contribution_c,subclusterPS:self_contribution_c)                  7772
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)     7191
## cor(Intercept,subclusterSS:self_contribution_c)                            9499
## cor(subclusterEM,subclusterSS:self_contribution_c)                         5304
## cor(subclusterPS,subclusterSS:self_contribution_c)                         5620
## cor(subclusterSS,subclusterSS:self_contribution_c)                         5382
## cor(self_contribution_c,subclusterSS:self_contribution_c)                  5784
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)     5530
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)     6413
##                                                                        Tail_ESS
## sd(Intercept)                                                              3673
## sd(subclusterEM)                                                           2920
## sd(subclusterPS)                                                           2688
## sd(subclusterSS)                                                           4026
## sd(self_contribution_c)                                                    1307
## sd(subclusterEM:self_contribution_c)                                       3816
## sd(subclusterPS:self_contribution_c)                                       4028
## sd(subclusterSS:self_contribution_c)                                       3174
## cor(Intercept,subclusterEM)                                                7808
## cor(Intercept,subclusterPS)                                                8539
## cor(subclusterEM,subclusterPS)                                             7310
## cor(Intercept,subclusterSS)                                                8335
## cor(subclusterEM,subclusterSS)                                             7962
## cor(subclusterPS,subclusterSS)                                             8497
## cor(Intercept,self_contribution_c)                                         5735
## cor(subclusterEM,self_contribution_c)                                      4206
## cor(subclusterPS,self_contribution_c)                                      4941
## cor(subclusterSS,self_contribution_c)                                      5246
## cor(Intercept,subclusterEM:self_contribution_c)                            8015
## cor(subclusterEM,subclusterEM:self_contribution_c)                         8099
## cor(subclusterPS,subclusterEM:self_contribution_c)                         7472
## cor(subclusterSS,subclusterEM:self_contribution_c)                         8529
## cor(self_contribution_c,subclusterEM:self_contribution_c)                  7625
## cor(Intercept,subclusterPS:self_contribution_c)                            7556
## cor(subclusterEM,subclusterPS:self_contribution_c)                         7675
## cor(subclusterPS,subclusterPS:self_contribution_c)                         8215
## cor(subclusterSS,subclusterPS:self_contribution_c)                         8550
## cor(self_contribution_c,subclusterPS:self_contribution_c)                  9205
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)     9946
## cor(Intercept,subclusterSS:self_contribution_c)                            7399
## cor(subclusterEM,subclusterSS:self_contribution_c)                         8153
## cor(subclusterPS,subclusterSS:self_contribution_c)                         7956
## cor(subclusterSS,subclusterSS:self_contribution_c)                         8706
## cor(self_contribution_c,subclusterSS:self_contribution_c)                  8391
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)     9014
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)     9236
## 
## ~word (Number of levels: 16) 
##                                    Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                          0.20      0.16     0.01     0.59 1.00
## sd(self_contribution_c)                0.01      0.01     0.00     0.04 1.00
## cor(Intercept,self_contribution_c)     0.05      0.58    -0.94     0.96 1.00
##                                    Bulk_ESS Tail_ESS
## sd(Intercept)                          3709     4927
## sd(self_contribution_c)                3750     5506
## cor(Intercept,self_contribution_c)     5917     7149
## 
## Population-Level Effects: 
##                                  Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1]                        -5.89      0.57    -7.10    -4.85 1.00
## Intercept[2]                        -1.99      0.39    -2.77    -1.25 1.00
## Intercept[3]                         0.90      0.37     0.17     1.64 1.00
## Intercept[4]                         3.33      0.44     2.51     4.23 1.00
## Intercept[5]                         6.39      0.63     5.25     7.73 1.00
## subclusterEM                         0.19      0.31    -0.42     0.82 1.00
## subclusterPS                        -0.15      0.33    -0.83     0.50 1.00
## subclusterSS                        -0.21      0.37    -0.95     0.50 1.00
## self_contribution_c                  0.05      0.02     0.02     0.08 1.00
## difficulty_c                        -0.03      0.01    -0.04    -0.02 1.00
## subclusterEM:self_contribution_c     0.00      0.02    -0.03     0.04 1.00
## subclusterPS:self_contribution_c    -0.01      0.02    -0.05     0.02 1.00
## subclusterSS:self_contribution_c    -0.01      0.02    -0.05     0.03 1.00
##                                  Bulk_ESS Tail_ESS
## Intercept[1]                         2068     3505
## Intercept[2]                         3008     5389
## Intercept[3]                         3586     5811
## Intercept[4]                         2752     4473
## Intercept[5]                         2093     3827
## subclusterEM                         7493     7629
## subclusterPS                         6814     6820
## subclusterSS                         7314     7038
## self_contribution_c                  3414     4673
## difficulty_c                         5799     6579
## subclusterEM:self_contribution_c     5913     6703
## subclusterPS:self_contribution_c     5466     6859
## subclusterSS:self_contribution_c     5966     7099
## 
## Family Specific Parameters: 
##      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc     1.00      0.00     1.00     1.00   NA       NA       NA
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(IOS_subset_self_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0    -0.03      0.01    -0.04    -0.02        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_subset_self_mdl,
           'self_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0     0.05      0.02     0.03     0.08     922.08
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_subset_self_mdl,
           'subclusterEM:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:sel... < 0        0      0.02    -0.03     0.03       0.83
##   Post.Prob Star
## 1      0.45     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_subset_self_mdl,
           'subclusterPS:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:sel... < 0    -0.01      0.02    -0.05     0.02       3.73
##   Post.Prob Star
## 1      0.79     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(IOS_subset_self_mdl,
           'subclusterSS:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:sel... < 0    -0.01      0.02    -0.04     0.03       1.82
##   Post.Prob Star
## 1      0.65     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Next, the distance on other model for only the abstract concepts.

dist_subset_other_mdl <- brm(bf(closeness_01 ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        other_contribution_c +
                        difficulty_c +
                        subcluster:other_contribution_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           other_contribution_c +
                           subcluster:other_contribution_c|participant) +
                        (1 + other_contribution_c|word),
                        phi ~ 1),
           
                      data = filter(df, category == 'abstract'),
                      family = Beta,
           
                      # MCMC settings:
                               
                      init = 0,
                      seed = 42,
                      cores = 4,
                      iter = 7500,
                      warmup = 3500,
                      save_pars = save_pars(all = TRUE), # for bayes factors
                      control = list(adapt_delta = 0.99))

# Save model:

save(dist_subset_other_mdl,
     file = '../models_E2/dist_subset_other_mdl.Rdata')

Corresponding null model:

dist_subset_other_null <- brm(bf(closeness_01 ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        other_contribution_c +
                        difficulty_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           other_contribution_c +
                           subcluster:other_contribution_c|participant) +
                        (1 + other_contribution_c|word),
                        phi ~ 1),
           
                      data = filter(df, category == 'abstract'),
                      family = Beta,
           
                      # MCMC settings:
                               
                      init = 0,
                      seed = 42,
                      cores = 4,
                      iter = 7500,
                      warmup = 3500,
                      save_pars = save_pars(all = TRUE), # for bayes factors
                      control = list(adapt_delta = 0.99))

# Save model:

save(dist_subset_other_null,
     file = '../models_E2/dist_subset_other_null.Rdata')

Load model:

load('../models_E2/dist_subset_other_mdl.Rdata')
load('../models_E2/dist_subset_other_null.Rdata')

Show priors:

prior_summary(dist_subset_other_mdl)
##                 prior     class                              coef       group
##                (flat)         b                                              
##                (flat)         b                      difficulty_c            
##                (flat)         b              other_contribution_c            
##                (flat)         b                      subclusterEM            
##                (flat)         b subclusterEM:other_contribution_c            
##                (flat)         b                      subclusterPS            
##                (flat)         b subclusterPS:other_contribution_c            
##                (flat)         b                      subclusterSS            
##                (flat)         b subclusterSS:other_contribution_c            
##  student_t(3, 0, 2.5) Intercept                                              
##  student_t(3, 0, 2.5) Intercept                                              
##  lkj_corr_cholesky(1)         L                                              
##  lkj_corr_cholesky(1)         L                                   participant
##  lkj_corr_cholesky(1)         L                                          word
##  student_t(3, 0, 2.5)        sd                                              
##  student_t(3, 0, 2.5)        sd                                   participant
##  student_t(3, 0, 2.5)        sd                         Intercept participant
##  student_t(3, 0, 2.5)        sd              other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterEM participant
##  student_t(3, 0, 2.5)        sd subclusterEM:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterPS participant
##  student_t(3, 0, 2.5)        sd subclusterPS:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterSS participant
##  student_t(3, 0, 2.5)        sd subclusterSS:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                                          word
##  student_t(3, 0, 2.5)        sd                         Intercept        word
##  student_t(3, 0, 2.5)        sd              other_contribution_c        word
##  resp dpar nlpar lb ub       source
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##        phi                  default
##                             default
##                        (vectorized)
##                        (vectorized)
##                   0         default
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
prior_summary(dist_subset_other_null)
##                 prior     class                              coef       group
##                (flat)         b                                              
##                (flat)         b                      difficulty_c            
##                (flat)         b              other_contribution_c            
##                (flat)         b                      subclusterEM            
##                (flat)         b                      subclusterPS            
##                (flat)         b                      subclusterSS            
##  student_t(3, 0, 2.5) Intercept                                              
##  student_t(3, 0, 2.5) Intercept                                              
##  lkj_corr_cholesky(1)         L                                              
##  lkj_corr_cholesky(1)         L                                   participant
##  lkj_corr_cholesky(1)         L                                          word
##  student_t(3, 0, 2.5)        sd                                              
##  student_t(3, 0, 2.5)        sd                                   participant
##  student_t(3, 0, 2.5)        sd                         Intercept participant
##  student_t(3, 0, 2.5)        sd              other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterEM participant
##  student_t(3, 0, 2.5)        sd subclusterEM:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterPS participant
##  student_t(3, 0, 2.5)        sd subclusterPS:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                      subclusterSS participant
##  student_t(3, 0, 2.5)        sd subclusterSS:other_contribution_c participant
##  student_t(3, 0, 2.5)        sd                                          word
##  student_t(3, 0, 2.5)        sd                         Intercept        word
##  student_t(3, 0, 2.5)        sd              other_contribution_c        word
##  resp dpar nlpar lb ub       source
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##        phi                  default
##                             default
##                        (vectorized)
##                        (vectorized)
##                   0         default
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)

Compute Bayes factor:

# Compute bayes factor:

dist_subset_bf <- bayes_factor(dist_subset_other_mdl, dist_subset_other_null)

# Save:

save(dist_subset_bf,
     file = '../models_E2/dist_subset_bf.RData')

Show Bayes factor:

# # Load:
# 
# load('../models_E2/IOS_subset_bf.RData')
# 
# # Show:
# 
# dist_subset_bf

Having some implementational issues here. Need to check the following warning message:

<<< Error in dyn.load(libLFile) : unable to load shared object ‘/var/folders/mn/d8pyxq412154r5dt7qg7s7rm0000gn/T//RtmpqOZ9uZ/file10301753938d.so’: dlopen(/var/folders/mn/d8pyxq412154r5dt7qg7s7rm0000gn/T//RtmpqOZ9uZ/file10301753938d.so, 6): Library not loaded: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libR.dylib Referenced from: /private/var/folders/mn/d8pyxq412154r5dt7qg7s7rm0000gn/T/RtmpqOZ9uZ/file10301753938d.so Reason: Incompatible library version: file10301753938d.so requires version 4.2.0 or later, but libR.dylib provides version 4.1.0 <<<

Check posterior predictive checks of the mixed beta regression:

pp_check(dist_subset_other_mdl, ndraws = 100)

Check this model:

dist_subset_other_mdl
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: closeness_01 ~ 1 + subcluster + other_contribution_c + difficulty_c + subcluster:other_contribution_c + (1 + subcluster + other_contribution_c + subcluster:other_contribution_c | participant) + (1 + other_contribution_c | word) 
##          phi ~ 1
##    Data: filter(df, category == "abstract") (Number of observations: 516) 
##   Draws: 4 chains, each with iter = 7500; warmup = 3500; thin = 1;
##          total post-warmup draws = 16000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                          Estimate
## sd(Intercept)                                                                0.85
## sd(subclusterEM)                                                             0.13
## sd(subclusterPS)                                                             0.31
## sd(subclusterSS)                                                             0.13
## sd(other_contribution_c)                                                     0.03
## sd(subclusterEM:other_contribution_c)                                        0.02
## sd(subclusterPS:other_contribution_c)                                        0.02
## sd(subclusterSS:other_contribution_c)                                        0.02
## cor(Intercept,subclusterEM)                                                 -0.00
## cor(Intercept,subclusterPS)                                                  0.14
## cor(subclusterEM,subclusterPS)                                              -0.01
## cor(Intercept,subclusterSS)                                                  0.03
## cor(subclusterEM,subclusterSS)                                               0.05
## cor(subclusterPS,subclusterSS)                                               0.23
## cor(Intercept,other_contribution_c)                                         -0.09
## cor(subclusterEM,other_contribution_c)                                       0.09
## cor(subclusterPS,other_contribution_c)                                      -0.28
## cor(subclusterSS,other_contribution_c)                                      -0.10
## cor(Intercept,subclusterEM:other_contribution_c)                             0.11
## cor(subclusterEM,subclusterEM:other_contribution_c)                          0.12
## cor(subclusterPS,subclusterEM:other_contribution_c)                         -0.08
## cor(subclusterSS,subclusterEM:other_contribution_c)                         -0.09
## cor(other_contribution_c,subclusterEM:other_contribution_c)                 -0.24
## cor(Intercept,subclusterPS:other_contribution_c)                             0.30
## cor(subclusterEM,subclusterPS:other_contribution_c)                         -0.05
## cor(subclusterPS,subclusterPS:other_contribution_c)                          0.35
## cor(subclusterSS,subclusterPS:other_contribution_c)                          0.21
## cor(other_contribution_c,subclusterPS:other_contribution_c)                 -0.35
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)     0.10
## cor(Intercept,subclusterSS:other_contribution_c)                            -0.14
## cor(subclusterEM,subclusterSS:other_contribution_c)                         -0.03
## cor(subclusterPS,subclusterSS:other_contribution_c)                          0.11
## cor(subclusterSS,subclusterSS:other_contribution_c)                          0.18
## cor(other_contribution_c,subclusterSS:other_contribution_c)                 -0.07
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)     0.38
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)     0.30
##                                                                          Est.Error
## sd(Intercept)                                                                 0.07
## sd(subclusterEM)                                                              0.09
## sd(subclusterPS)                                                              0.11
## sd(subclusterSS)                                                              0.09
## sd(other_contribution_c)                                                      0.00
## sd(subclusterEM:other_contribution_c)                                         0.00
## sd(subclusterPS:other_contribution_c)                                         0.01
## sd(subclusterSS:other_contribution_c)                                         0.01
## cor(Intercept,subclusterEM)                                                   0.28
## cor(Intercept,subclusterPS)                                                   0.21
## cor(subclusterEM,subclusterPS)                                                0.32
## cor(Intercept,subclusterSS)                                                   0.29
## cor(subclusterEM,subclusterSS)                                                0.33
## cor(subclusterPS,subclusterSS)                                                0.33
## cor(Intercept,other_contribution_c)                                           0.13
## cor(subclusterEM,other_contribution_c)                                        0.29
## cor(subclusterPS,other_contribution_c)                                        0.22
## cor(subclusterSS,other_contribution_c)                                        0.29
## cor(Intercept,subclusterEM:other_contribution_c)                              0.18
## cor(subclusterEM,subclusterEM:other_contribution_c)                           0.31
## cor(subclusterPS,subclusterEM:other_contribution_c)                           0.25
## cor(subclusterSS,subclusterEM:other_contribution_c)                           0.31
## cor(other_contribution_c,subclusterEM:other_contribution_c)                   0.21
## cor(Intercept,subclusterPS:other_contribution_c)                              0.19
## cor(subclusterEM,subclusterPS:other_contribution_c)                           0.32
## cor(subclusterPS,subclusterPS:other_contribution_c)                           0.22
## cor(subclusterSS,subclusterPS:other_contribution_c)                           0.33
## cor(other_contribution_c,subclusterPS:other_contribution_c)                   0.20
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)      0.23
## cor(Intercept,subclusterSS:other_contribution_c)                              0.23
## cor(subclusterEM,subclusterSS:other_contribution_c)                           0.32
## cor(subclusterPS,subclusterSS:other_contribution_c)                           0.30
## cor(subclusterSS,subclusterSS:other_contribution_c)                           0.32
## cor(other_contribution_c,subclusterSS:other_contribution_c)                   0.26
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)      0.26
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)      0.28
##                                                                          l-95% CI
## sd(Intercept)                                                                0.72
## sd(subclusterEM)                                                             0.00
## sd(subclusterPS)                                                             0.07
## sd(subclusterSS)                                                             0.01
## sd(other_contribution_c)                                                     0.02
## sd(subclusterEM:other_contribution_c)                                        0.01
## sd(subclusterPS:other_contribution_c)                                        0.01
## sd(subclusterSS:other_contribution_c)                                        0.00
## cor(Intercept,subclusterEM)                                                 -0.55
## cor(Intercept,subclusterPS)                                                 -0.25
## cor(subclusterEM,subclusterPS)                                              -0.63
## cor(Intercept,subclusterSS)                                                 -0.55
## cor(subclusterEM,subclusterSS)                                              -0.59
## cor(subclusterPS,subclusterSS)                                              -0.49
## cor(Intercept,other_contribution_c)                                         -0.35
## cor(subclusterEM,other_contribution_c)                                      -0.50
## cor(subclusterPS,other_contribution_c)                                      -0.68
## cor(subclusterSS,other_contribution_c)                                      -0.62
## cor(Intercept,subclusterEM:other_contribution_c)                            -0.26
## cor(subclusterEM,subclusterEM:other_contribution_c)                         -0.51
## cor(subclusterPS,subclusterEM:other_contribution_c)                         -0.56
## cor(subclusterSS,subclusterEM:other_contribution_c)                         -0.66
## cor(other_contribution_c,subclusterEM:other_contribution_c)                 -0.59
## cor(Intercept,subclusterPS:other_contribution_c)                            -0.08
## cor(subclusterEM,subclusterPS:other_contribution_c)                         -0.64
## cor(subclusterPS,subclusterPS:other_contribution_c)                         -0.12
## cor(subclusterSS,subclusterPS:other_contribution_c)                         -0.48
## cor(other_contribution_c,subclusterPS:other_contribution_c)                 -0.70
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)    -0.40
## cor(Intercept,subclusterSS:other_contribution_c)                            -0.56
## cor(subclusterEM,subclusterSS:other_contribution_c)                         -0.62
## cor(subclusterPS,subclusterSS:other_contribution_c)                         -0.51
## cor(subclusterSS,subclusterSS:other_contribution_c)                         -0.49
## cor(other_contribution_c,subclusterSS:other_contribution_c)                 -0.55
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)    -0.29
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)    -0.34
##                                                                          u-95% CI
## sd(Intercept)                                                                1.01
## sd(subclusterEM)                                                             0.33
## sd(subclusterPS)                                                             0.54
## sd(subclusterSS)                                                             0.32
## sd(other_contribution_c)                                                     0.04
## sd(subclusterEM:other_contribution_c)                                        0.03
## sd(subclusterPS:other_contribution_c)                                        0.04
## sd(subclusterSS:other_contribution_c)                                        0.03
## cor(Intercept,subclusterEM)                                                  0.56
## cor(Intercept,subclusterPS)                                                  0.57
## cor(subclusterEM,subclusterPS)                                               0.59
## cor(Intercept,subclusterSS)                                                  0.58
## cor(subclusterEM,subclusterSS)                                               0.66
## cor(subclusterPS,subclusterSS)                                               0.77
## cor(Intercept,other_contribution_c)                                          0.17
## cor(subclusterEM,other_contribution_c)                                       0.62
## cor(subclusterPS,other_contribution_c)                                       0.19
## cor(subclusterSS,other_contribution_c)                                       0.51
## cor(Intercept,subclusterEM:other_contribution_c)                             0.46
## cor(subclusterEM,subclusterEM:other_contribution_c)                          0.67
## cor(subclusterPS,subclusterEM:other_contribution_c)                          0.43
## cor(subclusterSS,subclusterEM:other_contribution_c)                          0.54
## cor(other_contribution_c,subclusterEM:other_contribution_c)                  0.21
## cor(Intercept,subclusterPS:other_contribution_c)                             0.66
## cor(subclusterEM,subclusterPS:other_contribution_c)                          0.60
## cor(subclusterPS,subclusterPS:other_contribution_c)                          0.75
## cor(subclusterSS,subclusterPS:other_contribution_c)                          0.76
## cor(other_contribution_c,subclusterPS:other_contribution_c)                  0.08
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)     0.52
## cor(Intercept,subclusterSS:other_contribution_c)                             0.34
## cor(subclusterEM,subclusterSS:other_contribution_c)                          0.59
## cor(subclusterPS,subclusterSS:other_contribution_c)                          0.65
## cor(subclusterSS,subclusterSS:other_contribution_c)                          0.72
## cor(other_contribution_c,subclusterSS:other_contribution_c)                  0.46
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)     0.76
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)     0.75
##                                                                          Rhat
## sd(Intercept)                                                            1.00
## sd(subclusterEM)                                                         1.00
## sd(subclusterPS)                                                         1.00
## sd(subclusterSS)                                                         1.00
## sd(other_contribution_c)                                                 1.00
## sd(subclusterEM:other_contribution_c)                                    1.00
## sd(subclusterPS:other_contribution_c)                                    1.00
## sd(subclusterSS:other_contribution_c)                                    1.00
## cor(Intercept,subclusterEM)                                              1.00
## cor(Intercept,subclusterPS)                                              1.00
## cor(subclusterEM,subclusterPS)                                           1.00
## cor(Intercept,subclusterSS)                                              1.00
## cor(subclusterEM,subclusterSS)                                           1.00
## cor(subclusterPS,subclusterSS)                                           1.00
## cor(Intercept,other_contribution_c)                                      1.00
## cor(subclusterEM,other_contribution_c)                                   1.00
## cor(subclusterPS,other_contribution_c)                                   1.00
## cor(subclusterSS,other_contribution_c)                                   1.00
## cor(Intercept,subclusterEM:other_contribution_c)                         1.00
## cor(subclusterEM,subclusterEM:other_contribution_c)                      1.00
## cor(subclusterPS,subclusterEM:other_contribution_c)                      1.00
## cor(subclusterSS,subclusterEM:other_contribution_c)                      1.00
## cor(other_contribution_c,subclusterEM:other_contribution_c)              1.00
## cor(Intercept,subclusterPS:other_contribution_c)                         1.00
## cor(subclusterEM,subclusterPS:other_contribution_c)                      1.00
## cor(subclusterPS,subclusterPS:other_contribution_c)                      1.00
## cor(subclusterSS,subclusterPS:other_contribution_c)                      1.00
## cor(other_contribution_c,subclusterPS:other_contribution_c)              1.00
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(Intercept,subclusterSS:other_contribution_c)                         1.00
## cor(subclusterEM,subclusterSS:other_contribution_c)                      1.00
## cor(subclusterPS,subclusterSS:other_contribution_c)                      1.00
## cor(subclusterSS,subclusterSS:other_contribution_c)                      1.00
## cor(other_contribution_c,subclusterSS:other_contribution_c)              1.00
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 1.00
##                                                                          Bulk_ESS
## sd(Intercept)                                                                3262
## sd(subclusterEM)                                                             1138
## sd(subclusterPS)                                                              855
## sd(subclusterSS)                                                             1532
## sd(other_contribution_c)                                                     3296
## sd(subclusterEM:other_contribution_c)                                        1093
## sd(subclusterPS:other_contribution_c)                                        1271
## sd(subclusterSS:other_contribution_c)                                         881
## cor(Intercept,subclusterEM)                                                 10047
## cor(Intercept,subclusterPS)                                                  3996
## cor(subclusterEM,subclusterPS)                                               1545
## cor(Intercept,subclusterSS)                                                 13487
## cor(subclusterEM,subclusterSS)                                               4040
## cor(subclusterPS,subclusterSS)                                               3306
## cor(Intercept,other_contribution_c)                                          4326
## cor(subclusterEM,other_contribution_c)                                        822
## cor(subclusterPS,other_contribution_c)                                       1480
## cor(subclusterSS,other_contribution_c)                                       1047
## cor(Intercept,subclusterEM:other_contribution_c)                             5320
## cor(subclusterEM,subclusterEM:other_contribution_c)                          1297
## cor(subclusterPS,subclusterEM:other_contribution_c)                          2105
## cor(subclusterSS,subclusterEM:other_contribution_c)                          1772
## cor(other_contribution_c,subclusterEM:other_contribution_c)                  3196
## cor(Intercept,subclusterPS:other_contribution_c)                             2980
## cor(subclusterEM,subclusterPS:other_contribution_c)                          1421
## cor(subclusterPS,subclusterPS:other_contribution_c)                          2473
## cor(subclusterSS,subclusterPS:other_contribution_c)                          1890
## cor(other_contribution_c,subclusterPS:other_contribution_c)                  4128
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)     2160
## cor(Intercept,subclusterSS:other_contribution_c)                             6215
## cor(subclusterEM,subclusterSS:other_contribution_c)                          2292
## cor(subclusterPS,subclusterSS:other_contribution_c)                          3005
## cor(subclusterSS,subclusterSS:other_contribution_c)                          2448
## cor(other_contribution_c,subclusterSS:other_contribution_c)                  4544
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)     1858
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)     3450
##                                                                          Tail_ESS
## sd(Intercept)                                                                5453
## sd(subclusterEM)                                                             2348
## sd(subclusterPS)                                                             1619
## sd(subclusterSS)                                                             3651
## sd(other_contribution_c)                                                     6559
## sd(subclusterEM:other_contribution_c)                                        1987
## sd(subclusterPS:other_contribution_c)                                        2708
## sd(subclusterSS:other_contribution_c)                                        1629
## cor(Intercept,subclusterEM)                                                  9596
## cor(Intercept,subclusterPS)                                                  6121
## cor(subclusterEM,subclusterPS)                                               4027
## cor(Intercept,subclusterSS)                                                 10556
## cor(subclusterEM,subclusterSS)                                               8287
## cor(subclusterPS,subclusterSS)                                               8845
## cor(Intercept,other_contribution_c)                                          8196
## cor(subclusterEM,other_contribution_c)                                       1553
## cor(subclusterPS,other_contribution_c)                                       2415
## cor(subclusterSS,other_contribution_c)                                       2343
## cor(Intercept,subclusterEM:other_contribution_c)                             6938
## cor(subclusterEM,subclusterEM:other_contribution_c)                          2733
## cor(subclusterPS,subclusterEM:other_contribution_c)                          4326
## cor(subclusterSS,subclusterEM:other_contribution_c)                          3863
## cor(other_contribution_c,subclusterEM:other_contribution_c)                  4580
## cor(Intercept,subclusterPS:other_contribution_c)                             5683
## cor(subclusterEM,subclusterPS:other_contribution_c)                          3467
## cor(subclusterPS,subclusterPS:other_contribution_c)                          4162
## cor(subclusterSS,subclusterPS:other_contribution_c)                          4533
## cor(other_contribution_c,subclusterPS:other_contribution_c)                  7002
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c)     3628
## cor(Intercept,subclusterSS:other_contribution_c)                             7479
## cor(subclusterEM,subclusterSS:other_contribution_c)                          5399
## cor(subclusterPS,subclusterSS:other_contribution_c)                          6433
## cor(subclusterSS,subclusterSS:other_contribution_c)                          4589
## cor(other_contribution_c,subclusterSS:other_contribution_c)                  8540
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c)     3287
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c)     5888
## 
## ~word (Number of levels: 16) 
##                                     Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                           0.06      0.04     0.00     0.16 1.00
## sd(other_contribution_c)                0.00      0.00     0.00     0.01 1.00
## cor(Intercept,other_contribution_c)     0.13      0.56    -0.91     0.97 1.00
##                                     Bulk_ESS Tail_ESS
## sd(Intercept)                           3007     5319
## sd(other_contribution_c)                4453     6921
## cor(Intercept,other_contribution_c)     6801     9617
## 
## Population-Level Effects: 
##                                   Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept                             0.98      0.10     0.79     1.16 1.00
## phi_Intercept                         4.13      0.20     3.76     4.51 1.00
## subclusterEM                         -0.04      0.07    -0.18     0.10 1.00
## subclusterPS                          0.01      0.08    -0.15     0.17 1.00
## subclusterSS                         -0.08      0.08    -0.24     0.08 1.00
## other_contribution_c                  0.02      0.00     0.01     0.02 1.00
## difficulty_c                         -0.00      0.00    -0.01    -0.00 1.00
## subclusterEM:other_contribution_c    -0.00      0.00    -0.01     0.01 1.00
## subclusterPS:other_contribution_c    -0.00      0.00    -0.01     0.01 1.00
## subclusterSS:other_contribution_c    -0.00      0.00    -0.01     0.01 1.00
##                                   Bulk_ESS Tail_ESS
## Intercept                             2168     4480
## phi_Intercept                          646     2162
## subclusterEM                          6863     6781
## subclusterPS                          6887     7389
## subclusterSS                          7373     7261
## other_contribution_c                  6324     8474
## difficulty_c                          7416    11110
## subclusterEM:other_contribution_c     5462     6721
## subclusterPS:other_contribution_c     7214     8040
## subclusterSS:other_contribution_c     6674     7911
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(dist_subset_other_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0        0         0    -0.01        0       1599         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_subset_other_mdl,
           'other_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0     0.02         0     0.01     0.02    1229.77
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_subset_other_mdl,
           'subclusterEM:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:oth... < 0        0         0    -0.01     0.01        1.8
##   Post.Prob Star
## 1      0.64     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_subset_other_mdl,
           'subclusterPS:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:oth... < 0        0         0    -0.01     0.01       2.43
##   Post.Prob Star
## 1      0.71     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_subset_other_mdl,
           'subclusterSS:other_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:oth... < 0        0         0    -0.01     0.01       2.18
##   Post.Prob Star
## 1      0.69     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Finally, the distance model with self contribution as covariate, again for only the abstract concepts.

dist_subset_self_mdl <- brm(bf(closeness_01 ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        self_contribution_c +
                        difficulty_c +
                        subcluster:self_contribution_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           self_contribution_c +
                           subcluster:self_contribution_c|participant) +
                        (1 + self_contribution_c|word),
                        phi ~ 1),
           
                      data = filter(df, category == 'abstract'),
                      family = Beta,
           
                      # MCMC settings:
                               
                      init = 0,
                      seed = 42,
                      cores = 4,
                      iter = 7500,
                      warmup = 3500, # higher because ESS low warning
                      save_pars = save_pars(all = TRUE), # for bayes factors
                      control = list(adapt_delta = 0.99))

# Save model:

save(dist_subset_self_mdl,
     file = '../models_E2/dist_subset_self_mdl.Rdata')

The corresponding null model:

dist_subset_self_null <- brm(bf(closeness_01 ~ 
                                 
                        # Fixed effects:
                                 
                        1 +
                        subcluster +
                        self_contribution_c +
                        difficulty_c +
                                 
                        # Random effects:
                                 
                        (1 +
                           subcluster +
                           self_contribution_c +
                           subcluster:self_contribution_c|participant) +
                        (1 + self_contribution_c|word),
                        phi ~ 1),
           
                      data = filter(df, category == 'abstract'),
                      family = Beta,
           
                      # MCMC settings:
                               
                      init = 0,
                      seed = 42,
                      cores = 4,
                      iter = 7500,
                      warmup = 3500, # higher because ESS low warning
                      save_pars = save_pars(all = TRUE), # for bayes factors
                      control = list(adapt_delta = 0.99))

# Save model:

save(dist_subset_self_null,
     file = '../models_E2/dist_subset_self_null.Rdata')

Load model:

load('../models_E2/dist_subset_self_mdl.Rdata')
load('../models_E2/dist_subset_self_null.Rdata')

Show priors:

prior_summary(dist_subset_self_mdl)
##                 prior     class                             coef       group
##                (flat)         b                                             
##                (flat)         b                     difficulty_c            
##                (flat)         b              self_contribution_c            
##                (flat)         b                     subclusterEM            
##                (flat)         b subclusterEM:self_contribution_c            
##                (flat)         b                     subclusterPS            
##                (flat)         b subclusterPS:self_contribution_c            
##                (flat)         b                     subclusterSS            
##                (flat)         b subclusterSS:self_contribution_c            
##  student_t(3, 0, 2.5) Intercept                                             
##  student_t(3, 0, 2.5) Intercept                                             
##  lkj_corr_cholesky(1)         L                                             
##  lkj_corr_cholesky(1)         L                                  participant
##  lkj_corr_cholesky(1)         L                                         word
##  student_t(3, 0, 2.5)        sd                                             
##  student_t(3, 0, 2.5)        sd                                  participant
##  student_t(3, 0, 2.5)        sd                        Intercept participant
##  student_t(3, 0, 2.5)        sd              self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterEM participant
##  student_t(3, 0, 2.5)        sd subclusterEM:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterPS participant
##  student_t(3, 0, 2.5)        sd subclusterPS:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterSS participant
##  student_t(3, 0, 2.5)        sd subclusterSS:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                                         word
##  student_t(3, 0, 2.5)        sd                        Intercept        word
##  student_t(3, 0, 2.5)        sd              self_contribution_c        word
##  resp dpar nlpar lb ub       source
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##        phi                  default
##                             default
##                        (vectorized)
##                        (vectorized)
##                   0         default
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
prior_summary(dist_subset_self_null)
##                 prior     class                             coef       group
##                (flat)         b                                             
##                (flat)         b                     difficulty_c            
##                (flat)         b              self_contribution_c            
##                (flat)         b                     subclusterEM            
##                (flat)         b                     subclusterPS            
##                (flat)         b                     subclusterSS            
##  student_t(3, 0, 2.5) Intercept                                             
##  student_t(3, 0, 2.5) Intercept                                             
##  lkj_corr_cholesky(1)         L                                             
##  lkj_corr_cholesky(1)         L                                  participant
##  lkj_corr_cholesky(1)         L                                         word
##  student_t(3, 0, 2.5)        sd                                             
##  student_t(3, 0, 2.5)        sd                                  participant
##  student_t(3, 0, 2.5)        sd                        Intercept participant
##  student_t(3, 0, 2.5)        sd              self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterEM participant
##  student_t(3, 0, 2.5)        sd subclusterEM:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterPS participant
##  student_t(3, 0, 2.5)        sd subclusterPS:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                     subclusterSS participant
##  student_t(3, 0, 2.5)        sd subclusterSS:self_contribution_c participant
##  student_t(3, 0, 2.5)        sd                                         word
##  student_t(3, 0, 2.5)        sd                        Intercept        word
##  student_t(3, 0, 2.5)        sd              self_contribution_c        word
##  resp dpar nlpar lb ub       source
##                             default
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                        (vectorized)
##                             default
##        phi                  default
##                             default
##                        (vectorized)
##                        (vectorized)
##                   0         default
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)
##                   0    (vectorized)

Compute Bayes factor:

# Compute bayes factor:

dist_subset_self_bf <- bayes_factor(dist_subset_self_mdl.Rdata,
                                    dist_subset_self_null)

# Save:

save(dist_self_bf,
     file = '../models_E2/dist_subset_self_bf.RData')

Same as above with the error…

Show Bayes factor:

# # Load:
# 
# load('../models_E2/dist_subset_self_bf.RData')
# 
# # Show:
# 
# dist_subset_self_bf

Check posterior predictive checks of the mixed beta regression:

pp_check(dist_subset_self_mdl, ndraws = 100)

Check this model:

dist_subset_self_mdl
##  Family: beta 
##   Links: mu = logit; phi = log 
## Formula: closeness_01 ~ 1 + subcluster + self_contribution_c + difficulty_c + subcluster:self_contribution_c + (1 + subcluster + self_contribution_c + subcluster:self_contribution_c | participant) + (1 + self_contribution_c | word) 
##          phi ~ 1
##    Data: filter(df, category == "abstract") (Number of observations: 516) 
##   Draws: 4 chains, each with iter = 7500; warmup = 3500; thin = 1;
##          total post-warmup draws = 16000
## 
## Group-Level Effects: 
## ~participant (Number of levels: 129) 
##                                                                        Estimate
## sd(Intercept)                                                              0.87
## sd(subclusterEM)                                                           0.50
## sd(subclusterPS)                                                           0.71
## sd(subclusterSS)                                                           0.33
## sd(self_contribution_c)                                                    0.03
## sd(subclusterEM:self_contribution_c)                                       0.01
## sd(subclusterPS:self_contribution_c)                                       0.02
## sd(subclusterSS:self_contribution_c)                                       0.01
## cor(Intercept,subclusterEM)                                               -0.26
## cor(Intercept,subclusterPS)                                               -0.13
## cor(subclusterEM,subclusterPS)                                             0.34
## cor(Intercept,subclusterSS)                                               -0.15
## cor(subclusterEM,subclusterSS)                                             0.53
## cor(subclusterPS,subclusterSS)                                             0.54
## cor(Intercept,self_contribution_c)                                        -0.04
## cor(subclusterEM,self_contribution_c)                                      0.28
## cor(subclusterPS,self_contribution_c)                                      0.18
## cor(subclusterSS,self_contribution_c)                                      0.52
## cor(Intercept,subclusterEM:self_contribution_c)                           -0.05
## cor(subclusterEM,subclusterEM:self_contribution_c)                         0.44
## cor(subclusterPS,subclusterEM:self_contribution_c)                         0.01
## cor(subclusterSS,subclusterEM:self_contribution_c)                         0.15
## cor(self_contribution_c,subclusterEM:self_contribution_c)                 -0.07
## cor(Intercept,subclusterPS:self_contribution_c)                            0.26
## cor(subclusterEM,subclusterPS:self_contribution_c)                        -0.14
## cor(subclusterPS,subclusterPS:self_contribution_c)                         0.48
## cor(subclusterSS,subclusterPS:self_contribution_c)                         0.10
## cor(self_contribution_c,subclusterPS:self_contribution_c)                 -0.18
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)    -0.04
## cor(Intercept,subclusterSS:self_contribution_c)                           -0.34
## cor(subclusterEM,subclusterSS:self_contribution_c)                         0.18
## cor(subclusterPS,subclusterSS:self_contribution_c)                         0.19
## cor(subclusterSS,subclusterSS:self_contribution_c)                         0.28
## cor(self_contribution_c,subclusterSS:self_contribution_c)                  0.18
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)     0.16
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)     0.02
##                                                                        Est.Error
## sd(Intercept)                                                               0.07
## sd(subclusterEM)                                                            0.07
## sd(subclusterPS)                                                            0.08
## sd(subclusterSS)                                                            0.08
## sd(self_contribution_c)                                                     0.00
## sd(subclusterEM:self_contribution_c)                                        0.00
## sd(subclusterPS:self_contribution_c)                                        0.01
## sd(subclusterSS:self_contribution_c)                                        0.00
## cor(Intercept,subclusterEM)                                                 0.12
## cor(Intercept,subclusterPS)                                                 0.13
## cor(subclusterEM,subclusterPS)                                              0.13
## cor(Intercept,subclusterSS)                                                 0.18
## cor(subclusterEM,subclusterSS)                                              0.17
## cor(subclusterPS,subclusterSS)                                              0.18
## cor(Intercept,self_contribution_c)                                          0.14
## cor(subclusterEM,self_contribution_c)                                       0.15
## cor(subclusterPS,self_contribution_c)                                       0.15
## cor(subclusterSS,self_contribution_c)                                       0.19
## cor(Intercept,subclusterEM:self_contribution_c)                             0.27
## cor(subclusterEM,subclusterEM:self_contribution_c)                          0.26
## cor(subclusterPS,subclusterEM:self_contribution_c)                          0.28
## cor(subclusterSS,subclusterEM:self_contribution_c)                          0.29
## cor(self_contribution_c,subclusterEM:self_contribution_c)                   0.28
## cor(Intercept,subclusterPS:self_contribution_c)                             0.23
## cor(subclusterEM,subclusterPS:self_contribution_c)                          0.25
## cor(subclusterPS,subclusterPS:self_contribution_c)                          0.21
## cor(subclusterSS,subclusterPS:self_contribution_c)                          0.28
## cor(self_contribution_c,subclusterPS:self_contribution_c)                   0.25
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)      0.30
## cor(Intercept,subclusterSS:self_contribution_c)                             0.27
## cor(subclusterEM,subclusterSS:self_contribution_c)                          0.28
## cor(subclusterPS,subclusterSS:self_contribution_c)                          0.30
## cor(subclusterSS,subclusterSS:self_contribution_c)                          0.30
## cor(self_contribution_c,subclusterSS:self_contribution_c)                   0.28
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)      0.32
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)      0.31
##                                                                        l-95% CI
## sd(Intercept)                                                              0.73
## sd(subclusterEM)                                                           0.36
## sd(subclusterPS)                                                           0.55
## sd(subclusterSS)                                                           0.15
## sd(self_contribution_c)                                                    0.02
## sd(subclusterEM:self_contribution_c)                                       0.00
## sd(subclusterPS:self_contribution_c)                                       0.00
## sd(subclusterSS:self_contribution_c)                                       0.00
## cor(Intercept,subclusterEM)                                               -0.48
## cor(Intercept,subclusterPS)                                               -0.36
## cor(subclusterEM,subclusterPS)                                             0.06
## cor(Intercept,subclusterSS)                                               -0.47
## cor(subclusterEM,subclusterSS)                                             0.13
## cor(subclusterPS,subclusterSS)                                             0.13
## cor(Intercept,self_contribution_c)                                        -0.31
## cor(subclusterEM,self_contribution_c)                                     -0.04
## cor(subclusterPS,self_contribution_c)                                     -0.11
## cor(subclusterSS,self_contribution_c)                                      0.09
## cor(Intercept,subclusterEM:self_contribution_c)                           -0.58
## cor(subclusterEM,subclusterEM:self_contribution_c)                        -0.18
## cor(subclusterPS,subclusterEM:self_contribution_c)                        -0.52
## cor(subclusterSS,subclusterEM:self_contribution_c)                        -0.46
## cor(self_contribution_c,subclusterEM:self_contribution_c)                 -0.59
## cor(Intercept,subclusterPS:self_contribution_c)                           -0.24
## cor(subclusterEM,subclusterPS:self_contribution_c)                        -0.59
## cor(subclusterPS,subclusterPS:self_contribution_c)                        -0.02
## cor(subclusterSS,subclusterPS:self_contribution_c)                        -0.47
## cor(self_contribution_c,subclusterPS:self_contribution_c)                 -0.62
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)    -0.61
## cor(Intercept,subclusterSS:self_contribution_c)                           -0.78
## cor(subclusterEM,subclusterSS:self_contribution_c)                        -0.42
## cor(subclusterPS,subclusterSS:self_contribution_c)                        -0.45
## cor(subclusterSS,subclusterSS:self_contribution_c)                        -0.39
## cor(self_contribution_c,subclusterSS:self_contribution_c)                 -0.42
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)    -0.50
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)    -0.59
##                                                                        u-95% CI
## sd(Intercept)                                                              1.01
## sd(subclusterEM)                                                           0.63
## sd(subclusterPS)                                                           0.87
## sd(subclusterSS)                                                           0.48
## sd(self_contribution_c)                                                    0.03
## sd(subclusterEM:self_contribution_c)                                       0.02
## sd(subclusterPS:self_contribution_c)                                       0.03
## sd(subclusterSS:self_contribution_c)                                       0.02
## cor(Intercept,subclusterEM)                                               -0.00
## cor(Intercept,subclusterPS)                                                0.13
## cor(subclusterEM,subclusterPS)                                             0.58
## cor(Intercept,subclusterSS)                                                0.23
## cor(subclusterEM,subclusterSS)                                             0.80
## cor(subclusterPS,subclusterSS)                                             0.83
## cor(Intercept,self_contribution_c)                                         0.25
## cor(subclusterEM,self_contribution_c)                                      0.57
## cor(subclusterPS,self_contribution_c)                                      0.45
## cor(subclusterSS,self_contribution_c)                                      0.83
## cor(Intercept,subclusterEM:self_contribution_c)                            0.49
## cor(subclusterEM,subclusterEM:self_contribution_c)                         0.83
## cor(subclusterPS,subclusterEM:self_contribution_c)                         0.54
## cor(subclusterSS,subclusterEM:self_contribution_c)                         0.68
## cor(self_contribution_c,subclusterEM:self_contribution_c)                  0.51
## cor(Intercept,subclusterPS:self_contribution_c)                            0.65
## cor(subclusterEM,subclusterPS:self_contribution_c)                         0.39
## cor(subclusterPS,subclusterPS:self_contribution_c)                         0.81
## cor(subclusterSS,subclusterPS:self_contribution_c)                         0.63
## cor(self_contribution_c,subclusterPS:self_contribution_c)                  0.36
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)     0.53
## cor(Intercept,subclusterSS:self_contribution_c)                            0.29
## cor(subclusterEM,subclusterSS:self_contribution_c)                         0.67
## cor(subclusterPS,subclusterSS:self_contribution_c)                         0.71
## cor(subclusterSS,subclusterSS:self_contribution_c)                         0.77
## cor(self_contribution_c,subclusterSS:self_contribution_c)                  0.68
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)     0.71
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)     0.60
##                                                                        Rhat
## sd(Intercept)                                                          1.00
## sd(subclusterEM)                                                       1.00
## sd(subclusterPS)                                                       1.00
## sd(subclusterSS)                                                       1.00
## sd(self_contribution_c)                                                1.00
## sd(subclusterEM:self_contribution_c)                                   1.00
## sd(subclusterPS:self_contribution_c)                                   1.00
## sd(subclusterSS:self_contribution_c)                                   1.00
## cor(Intercept,subclusterEM)                                            1.00
## cor(Intercept,subclusterPS)                                            1.00
## cor(subclusterEM,subclusterPS)                                         1.00
## cor(Intercept,subclusterSS)                                            1.00
## cor(subclusterEM,subclusterSS)                                         1.00
## cor(subclusterPS,subclusterSS)                                         1.00
## cor(Intercept,self_contribution_c)                                     1.00
## cor(subclusterEM,self_contribution_c)                                  1.00
## cor(subclusterPS,self_contribution_c)                                  1.00
## cor(subclusterSS,self_contribution_c)                                  1.00
## cor(Intercept,subclusterEM:self_contribution_c)                        1.00
## cor(subclusterEM,subclusterEM:self_contribution_c)                     1.00
## cor(subclusterPS,subclusterEM:self_contribution_c)                     1.00
## cor(subclusterSS,subclusterEM:self_contribution_c)                     1.00
## cor(self_contribution_c,subclusterEM:self_contribution_c)              1.00
## cor(Intercept,subclusterPS:self_contribution_c)                        1.00
## cor(subclusterEM,subclusterPS:self_contribution_c)                     1.00
## cor(subclusterPS,subclusterPS:self_contribution_c)                     1.00
## cor(subclusterSS,subclusterPS:self_contribution_c)                     1.00
## cor(self_contribution_c,subclusterPS:self_contribution_c)              1.00
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(Intercept,subclusterSS:self_contribution_c)                        1.00
## cor(subclusterEM,subclusterSS:self_contribution_c)                     1.00
## cor(subclusterPS,subclusterSS:self_contribution_c)                     1.00
## cor(subclusterSS,subclusterSS:self_contribution_c)                     1.00
## cor(self_contribution_c,subclusterSS:self_contribution_c)              1.00
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 1.00
##                                                                        Bulk_ESS
## sd(Intercept)                                                              3559
## sd(subclusterEM)                                                           1720
## sd(subclusterPS)                                                           1513
## sd(subclusterSS)                                                           1534
## sd(self_contribution_c)                                                    3236
## sd(subclusterEM:self_contribution_c)                                       2469
## sd(subclusterPS:self_contribution_c)                                       1747
## sd(subclusterSS:self_contribution_c)                                       2140
## cor(Intercept,subclusterEM)                                                5067
## cor(Intercept,subclusterPS)                                                2865
## cor(subclusterEM,subclusterPS)                                             2371
## cor(Intercept,subclusterSS)                                                5771
## cor(subclusterEM,subclusterSS)                                             4361
## cor(subclusterPS,subclusterSS)                                             3584
## cor(Intercept,self_contribution_c)                                         4973
## cor(subclusterEM,self_contribution_c)                                      4070
## cor(subclusterPS,self_contribution_c)                                      4849
## cor(subclusterSS,self_contribution_c)                                      1763
## cor(Intercept,subclusterEM:self_contribution_c)                            8604
## cor(subclusterEM,subclusterEM:self_contribution_c)                         5657
## cor(subclusterPS,subclusterEM:self_contribution_c)                         9411
## cor(subclusterSS,subclusterEM:self_contribution_c)                         6820
## cor(self_contribution_c,subclusterEM:self_contribution_c)                  9119
## cor(Intercept,subclusterPS:self_contribution_c)                            4880
## cor(subclusterEM,subclusterPS:self_contribution_c)                         5640
## cor(subclusterPS,subclusterPS:self_contribution_c)                         5918
## cor(subclusterSS,subclusterPS:self_contribution_c)                         4754
## cor(self_contribution_c,subclusterPS:self_contribution_c)                  5162
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)     6680
## cor(Intercept,subclusterSS:self_contribution_c)                            7812
## cor(subclusterEM,subclusterSS:self_contribution_c)                         9184
## cor(subclusterPS,subclusterSS:self_contribution_c)                         9095
## cor(subclusterSS,subclusterSS:self_contribution_c)                         5466
## cor(self_contribution_c,subclusterSS:self_contribution_c)                 11519
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)     6897
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)     9511
##                                                                        Tail_ESS
## sd(Intercept)                                                              6898
## sd(subclusterEM)                                                           2520
## sd(subclusterPS)                                                           2731
## sd(subclusterSS)                                                           1817
## sd(self_contribution_c)                                                    5554
## sd(subclusterEM:self_contribution_c)                                       4103
## sd(subclusterPS:self_contribution_c)                                       2379
## sd(subclusterSS:self_contribution_c)                                       5199
## cor(Intercept,subclusterEM)                                                6795
## cor(Intercept,subclusterPS)                                                4104
## cor(subclusterEM,subclusterPS)                                             3825
## cor(Intercept,subclusterSS)                                                6289
## cor(subclusterEM,subclusterSS)                                             4691
## cor(subclusterPS,subclusterSS)                                             4804
## cor(Intercept,self_contribution_c)                                         8677
## cor(subclusterEM,self_contribution_c)                                      6765
## cor(subclusterPS,self_contribution_c)                                      8836
## cor(subclusterSS,self_contribution_c)                                      1967
## cor(Intercept,subclusterEM:self_contribution_c)                           11469
## cor(subclusterEM,subclusterEM:self_contribution_c)                         7332
## cor(subclusterPS,subclusterEM:self_contribution_c)                        11221
## cor(subclusterSS,subclusterEM:self_contribution_c)                        10010
## cor(self_contribution_c,subclusterEM:self_contribution_c)                 11852
## cor(Intercept,subclusterPS:self_contribution_c)                            6790
## cor(subclusterEM,subclusterPS:self_contribution_c)                         8355
## cor(subclusterPS,subclusterPS:self_contribution_c)                         6732
## cor(subclusterSS,subclusterPS:self_contribution_c)                         8699
## cor(self_contribution_c,subclusterPS:self_contribution_c)                  8018
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c)    11127
## cor(Intercept,subclusterSS:self_contribution_c)                            8763
## cor(subclusterEM,subclusterSS:self_contribution_c)                         9689
## cor(subclusterPS,subclusterSS:self_contribution_c)                        10743
## cor(subclusterSS,subclusterSS:self_contribution_c)                         8895
## cor(self_contribution_c,subclusterSS:self_contribution_c)                 10366
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c)    11853
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c)    12206
## 
## ~word (Number of levels: 16) 
##                                    Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept)                          0.06      0.04     0.00     0.17 1.00
## sd(self_contribution_c)                0.00      0.00     0.00     0.01 1.00
## cor(Intercept,self_contribution_c)     0.22      0.56    -0.90     0.98 1.00
##                                    Bulk_ESS Tail_ESS
## sd(Intercept)                          2869     5843
## sd(self_contribution_c)                4163     6858
## cor(Intercept,self_contribution_c)     6576     8996
## 
## Population-Level Effects: 
##                                  Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept                            1.02      0.10     0.83     1.21 1.00
## phi_Intercept                        4.36      0.22     3.92     4.78 1.01
## subclusterEM                        -0.05      0.08    -0.21     0.11 1.00
## subclusterPS                        -0.05      0.10    -0.24     0.14 1.00
## subclusterSS                        -0.05      0.08    -0.22     0.10 1.00
## self_contribution_c                  0.01      0.00     0.00     0.02 1.00
## difficulty_c                        -0.00      0.00    -0.01    -0.00 1.00
## subclusterEM:self_contribution_c    -0.00      0.00    -0.01     0.01 1.00
## subclusterPS:self_contribution_c    -0.01      0.01    -0.02     0.00 1.00
## subclusterSS:self_contribution_c    -0.00      0.00    -0.01     0.01 1.00
##                                  Bulk_ESS Tail_ESS
## Intercept                            3447     6424
## phi_Intercept                         805     1511
## subclusterEM                         7408     9170
## subclusterPS                         6067     8135
## subclusterSS                         8400     8531
## self_contribution_c                  6915     9556
## difficulty_c                         7781    11003
## subclusterEM:self_contribution_c     6990     9443
## subclusterPS:self_contribution_c     6790     9282
## subclusterSS:self_contribution_c     8179     9742
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Perform hypothesis tests on the fixed effects coefficient:

hypothesis(dist_subset_self_mdl,
           'difficulty_c < 0')
## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0        0         0    -0.01        0    1332.33         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_subset_self_mdl,
           'self_contribution_c > 0')
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0     0.01         0     0.01     0.02     614.38
##   Post.Prob Star
## 1         1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_subset_self_mdl,
           'subclusterEM:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:sel... < 0        0         0    -0.01        0       2.04
##   Post.Prob Star
## 1      0.67     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_subset_self_mdl,
           'subclusterPS:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:sel... < 0    -0.01      0.01    -0.01        0       5.67
##   Post.Prob Star
## 1      0.85     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
hypothesis(dist_subset_self_mdl,
           'subclusterSS:self_contribution_c < 0') # PSTQ is reference
## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:sel... < 0        0         0    -0.01        0       2.57
##   Post.Prob Star
## 1      0.72     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

This completes this analysis.